Keywords:Optimization, Optimization algorithms Abstract: This paper examines the nonconvex quadratically constrained quadratic programming (QCQP) problem using a complementary cutting plane method. It is well known that a QCQP can be transformed into an equivalent rank-one constrained optimization problem. Thus, we focus on searching the optimal rank-one matrix to minimize the objective while satisfying other linear matrix constraints. However, finding a rank-one matrix is computationally complicated. A cost-driven cutting plane (CDCP) method has been developed to gradually approach the rank-one constraint. To improve computational efficiency, a complementary cutting plane approach (CCPA) combing conventional intersection cut and cost-driven cut is proposed to solve QCQPs. In this new approach, a linear constraint is generated in each iteration to tighten the searching domain for a semidefinite programming problem generated from the cost-driven cut method. We further prove that adding the intersection cut in each iteration will not exclude any rank-one solution. Numerical examples with comparative results are presented and compared to verify the effectiveness and efficiency of the proposed approach.

Keywords:Optimization, Optimization algorithms Abstract: In this paper we propose an algorithm for solving constrained polynomial minimization problems. The algorithm is a variation on the random coordinate descent, in which transverse steps are sometimes taken. Differently from other methods, the proposed technique is guaranteed to converge in probability to the global solution of the minimization problem, even when the objective polynomial is nonconvex. The technique appears to be promising for tackling nonlinear control problems in which the standard Sum-of-Squares methods may fail due to the problem size. The theoretical results are corroborated by numerical tests that validate the efficiency of the method.

Keywords:Optimization, Networked control systems, Kalman filtering Abstract: We analyze the asymptotic nonanticipative rate distortion function (NRDF) of vector-valued Gauss-Markov processes subject to a mean-squared error (MSE) distortion function. We derive a parametric characterization in terms of a reverse-waterfilling algorithm, that requires the solution of a matrix Riccati algebraic equation (RAE). Further, we develop an algorithm reminiscent of the classical reverse-waterfilling algorithm that provides an upper bound to the optimal solution of the reverse-waterfilling optimization problem, and under certain cases, it operates at the NRDF. Moreover, using the characterization of the reverse-waterfilling algorithm, we derive the analytical solution of the NRDF, for a simple two-dimensional parallel Gauss-Markov process. The efficacy of our proposed algorithm is demonstrated via an example.

Keywords:Optimization, Adaptive control Abstract: We consider perturbation-based extremum seeking, which recovers an approximate gradient of an analytically unknown objective function through measurements. Using classical needle variation analysis, we are able to explicitly quantify the recovered gradient in the scalar case. We reveal that it corresponds to an averaged gradient of the objective function, even for very general extremum seeking systems. From this, we create a recursion which represents the learning dynamics along the recovered gradient. These results give rise to the interpretation that extremum seeking actually optimizes a function other than the original one. From this insight emerges a new perspective on global optimization of functions with local extrema: because the gradient is averaged over a certain time period, local extrema might be evened out in the learning dynamics. Moreover, a multidimensional extension of the scalar results is given.

Keywords:Optimization, Learning, Estimation Abstract: Given a linear multivariate regression problem with block sparsity structure on the regression matrix, one popular approach for estimating its unknown parameter is block-regularization, where the sparsity of different blocks of the regression matrix is promoted by penalizing their ell_{infty}-norms. The main goal of this work is to characterize the properties of this estimator under high-dimensional scaling, where the growth rate of the dimension of the problem is comparable or even faster than that of the sample size. In particular, this work generalizes the existing non-asymptotic results on special instances of block-regularized estimators to the case where the unknown regression matrix has an arbitrary number of blocks each with a potentially different size. When the design matrix is deterministic, a sharp non-asymptotic rate is derived on the element-wise error of the proposed estimator. Furthermore, it is proven that the same error rate approximately holds for the block-regularized estimator when the design matrix is randomly generated, provided that the number of samples exceeds a lower bound. The accuracy of the proposed estimator is illustrated on several test cases.

Keywords:Optimal control, Large-scale systems Abstract: We consider controlling graph-based MDPs (GMDPs) with two special properties: (i) Anonymous Influence and (ii) Symmetry. Large-scale spatial processes such as wildfires, disease epidemics, opinion dynamics, and robot swarms are well modeled by GMDPs with these properties. We derive two efficient and scalable algorithms for computing approximately optimal control policies for large GMDPs with Anonymous Influence and Symmetry and derive sub-optimality bounds for these policies. Unlike prior work, our algorithms explicitly enforce a global control capacity constraint. Our methods scale linearly in the number of equivalence classes in the GMDP rather than the total number of MDPs in the graph. We demonstrate our methods in simulations of controlling a wildfire with a global fire retardant constraint and controlling an Ebola outbreak with a global medicine constraint. Our Ebola model is derived from data from the 2014 West Africa outbreak.

Keywords:Optimal control, Constrained control, Algebraic/geometric methods Abstract: In this article we present a geometric discrete-time Pontryagin maximum principle (PMP) on matrix Lie groups that incorporates frequency constraints on the controls in addition to pointwise constraints on the states and control actions directly at the stage of the problem formulation. This PMP gives first order necessary conditions for optimality, and leads to two-point boundary value problems that may be solved by shooting techniques to arrive at optimal trajectories. We validate our theoretical results with a numerical experiment on the attitude control of a spacecraft on the Lie group SO(3).

Keywords:Optimal control, Constrained control, Optimization algorithms Abstract: The article is focused on the necessary optimality condition in the form of Pontryagin's maximum principle for state constrained problems. A certain refinement to these conditions is made. More specifically, it has been noted that the measure-multiplier from the maximum principle is continuous under the regularity conditions imposed in cite{Pontryagin_1962}. The continuity of the measure-multiplier appears to be highly relevant for numerical implementations in the framework of indirect computational approach.

Keywords:Optimal control, Learning, Neural networks Abstract: This paper presents a near optimal event-based tracking control scheme for nonlinear continuous time systems. In order to simultaneously design the event-based sampling intervals and the control policy, the problem of designing the event-triggering mechanism and the feedback controller is posed as a min-max optimization problem. Using the resultant saddle point solution, the feedback control policy and the threshold for the event-based sampling condition is designed. The proposed control scheme is realized by approximating the solution to the associated Hamilton-Jacobi-Issac (HJI) equation using event-based neural networks (NN). The NN weights are updated using an impulsive update scheme. Extension of Lyapunov stability analysis for the impulsive hybrid dynamical system is utilized to prove the local ultimate boundedness of the tracking and NN weight estimation errors. Furthermore, Zeno free behavior of the event-triggering mechanism is guaranteed along with the numerical simulation to corroborate the analytical design.

Keywords:Optimal control, Nonlinear output feedback, Optimization algorithms Abstract: This paper constitutes a further generalization of the numerical solution approaches to Optimal Control Problems (OCPs) of systems evolving with state suprema. We study multidimensional control systems described by differential equations with the sup-operator in the right hand sides. A specific state-observer model and the linear type feedback control design under consideration imply a resulting closed-loop system that can formally be characterized as a multidimensional Functional Differential Equation (FDE) with delays. We study OCPs associated with the obtained FDEs and establish some fundamental solution properties of this class of problems. A particular structure of the resulting dynamic optimization problem makes it possible to consider the originally given sophisticated OCP in the framework of the nonlinear separate programming in some Euclidean spaces. This fact makes it possible to apply effective and relative simple splitting type computational algorithms to the initially given sophisticated OCPs for systems evolving with state suprema.

Keywords:Optimization, Optimal control, LMIs Abstract: This two-part paper is concerned with the problem of minimizing a linear objective function subject to a bilinear matrix inequality (BMI) constraint. In this part, we first consider a family of convex relaxations which transform BMI optimization problems into polynomial-time solvable surrogates. As an alternative to the state-of-the-art semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations, a computationally efficient parabolic relaxation is developed, which relies on convex quadratic constraints only. Next, we developed a family of penalty functions, which can be incorporated into the objective of SDP, SOCP, and parabolic relaxations to facilitate the recovery of feasible points for the original non-convex BMI optimization. Penalty terms can be constructed using any arbitrary initial point. We prove that if the initial point is sufficiently close to the feasible set, then the penalized relaxations are guaranteed to produce feasible points for the original BMI. In Part II of the paper, the efficacy of the proposed penalized convex relaxations is demonstrated on benchmark instances of H2 and Hinf optimal control synthesis problems.

Keywords:Optimal control, LMIs Abstract: The first part of this paper proposed a family of penalized convex relaxations for solving optimization problems with bilinear matrix inequality (BMI) constraints. In this part, we generalize our approach to a sequential scheme which starts from an arbitrary initial point (feasible or infeasible) and solves a sequence of penalized convex relaxations in order to find feasible and near-optimal solutions for BMI optimization problems. We evaluate the performance of the proposed method on the H2 and Hinfinity optimal controller design problems with both centralized and decentralized structures. The experimental results based on a variety of benchmark control plants demonstrate the promising performance of the proposed approach in comparison with the existing methods.

Keywords:Agents-based systems, Randomized algorithms, Stochastic systems Abstract: In this paper, the problem of solving linear algebraic equations of the form Ax=b among multi agents is considered. It is assumed that the interconnection graphs over which the agents communicate are random. It is assumed that each agent only knows a subset of rows of the partitioned matrix [A,b]. The problem is formulated such that this formulation does not require distribution dependency of random communication graphs. The random Krasnoselskii-Mann iterative algorithm is applied for almost sure convergence to a solution of the problem for any matrices A and b and any initial conditions of agents' states. The algorithm converges almost surely independently from the distribution and, therefore, is amenable to completely asynchronous operations withot B-connectivity assumption. Based on initial conditions of agents' states, we show that the limit point of the sequence generated by the algorithm is determined by the unique solution of a convex optimization problem independent from the distribution of random communication graphs.

Keywords:Agents-based systems, Sensor networks, Optimization algorithms Abstract: Multiway matching refers to the problem of establishing correspondences among a set of images from noisy pairwise correspondences, typically by exploiting cycle consistency. Existing approaches for multiway matching address the problem in a centralized setting. In this work, we propose a novel distributed optimization approach to multiway matching based on distributed projected gradient descent with constant step size. We rigorously analyze the convergence properties of our algorithm, specifically the range of the step size that guarantees convergence to a stationary point. We provide experimental evidence supporting that the proposed approach has performance comparable with the state of the art centralized approaches.

Keywords:Agents-based systems, Cooperative control, Control of networks Abstract: In this paper we present a novel method for constructing stochastic weighting matrices with the help of a finite sequence that can be chosen according to the application in a distributed manner. In addition, we propose three algorithms that determine how every agent decides on assigning these weights to its neighbours. Then, the so-called sequence weighting method is compared with other existing approaches for the special case of a one-dimensional lattice graph. For this purpose, we derive the characteristic polynomial of a quasi-Toeplitz matrix. Considering the sequence weighting method we calculate a bound for the second greatest eigenvalue that can be bounded away from 1 independent of the network size. Using a recently reported result about uniform packet loss, we show that bounds on the convergence speed not only hold in the loss-free case, but also when uniform packet loss occurs. Simulation results with non-uniform packet loss confirm a better performance using the sequence weighting method in comparison to existing strategies.

Keywords:Agents-based systems, Cooperative control, Networked control systems Abstract: We consider the problem of accelerating the convergence to consensus of a network of homogeneous high-order agents, through the injection of an additional control input performed by a leader. After a brief set-up description, we derive the characteristic polynomial of the resulting system under the leader’s control. We introduce the concept of leader controlled distributed consensus, by imposing that the leader’s action improves the convergence speed but does not affect the consensus value, except possibly for a scaling factor. Finally, we prove that, under certain assumptions, consensus can be achieved with arbitrary speed.

Keywords:Agents-based systems, Network analysis and control, Networked control systems Abstract: In this work we consider a nonlinear interconnected system describing a decision-making process in a community of agents characterized by the coexistence of collaborative and antagonistic interactions. The resulting signed graph is in general not structurally balanced. It is shown in the paper that the decision-making process is affected by the frustration of the signed graph, in the sense that a nontrivial decision can be reached only if the social commitment of the agents is high enough to win the disorder introduced by the frustration in the network. The higher the frustration of the graph, the higher the commitment strength required from the agents.

Keywords:Agents-based systems, Cooperative control, Neural networks Abstract: Rhythmic behaviors are widely observed in animal motions. A fundamental control mechanism for producing and regulating rhythmic movements is based on the Central Pattern Generator (CPG), which is a distributed network of neuronal oscillators. Mathematical models of CPGs can be useful as a basic component in feedback control designs to achieve oscillations. This paper develops a CPG model as a network of nonlinear oscillators described by ordinary differential equations with complex variables. The use of complex state variables simplifies the CPG design and makes it transparent how the network connectivity relates to the resulting oscillation pattern. We will provide a method for designing CPGs to achieve oscillations of prescribed frequency, amplitude, and phase as a stable limit cycle with guaranteed local convergence. Moreover, we show how the network can be designed to embed multiple limit cycles in the state space.

Keywords:Control over communications, Lyapunov methods, LMIs Abstract: This paper deals with the design of an event-triggering mechanism using local information for a linear system controlled by an observer-based feedback controller. The event-triggered control strategy is based on a new dynamic triggering mechanism, which is introduced through an internal dynamic variable. Sufficient conditions based on linear matrix inequalities are proposed to ensure the asymptotic stability of the closed loop together with the avoidance of Zeno behavior. A convex optimization problem leans on these conditions to determine the parameters of the event-trigger rule aiming at reducing the number of control updates. Discussion with respect to the simpler state feedback case is drawn.

Keywords:Control over communications, Information theory and control, Networked control systems Abstract: We consider the problem of estimating an undisturbed, scalar, linear process over a ``timing'' channel, namely a channel where information is communicated through the timestamps of the transmitted symbols. Each transmitted symbol is received at the decoder subject to a random delay. The encoder can encode messages in the holding times between successive transmissions and the decoder must decode the message from the inter-reception times of successive symbols. This set-up is analogous to a telephone system where a transmitter signals a phone call to the receiver through a ``ring" and, after the random time required to establish the connection, is aware of the ``ring" being received. We show that for the estimation error to converge to zero in probability, the timing capacity of the channel should be at least as large as the entropy rate of the process. In the case the symbol delays are exponentially distributed, we show a tight sufficient condition using a random-coding strategy.

Keywords:Networked control systems, Constrained control, Discrete event systems Abstract: In recent years, event and self-triggered control have been proposed as energy-aware control strategies to expand the life-time of battery powered devices in Networked Control Systems (NCSs). In contrast to the previous works in which their control objective is to achieve stability, this paper presents a novel energy-aware control scheme for achieving high level specifications, or more specifically, temporal logic specifications. Inspired by the standard hierarchical strategy that has been proposed in the field of formal control synthesis paradigm, we propose a new abstraction procedure for jointly synthesizing control and communication strategies, such that the communication reduction in NCSs and the satisfaction of the temporal logic specifications are guaranteed. The benefits of the proposal are illustrated through a numerical example.

Keywords:Networked control systems, Linear systems, Stochastic optimal control Abstract: A consistent event-triggered control (ETC) policy is defined as a policy that outperforms the performance of periodic control for the same average transmission rate and does not generate transmissions in the absence of disturbances. In this paper, we propose a threshold-based policy for periodic event-triggered control that is consistent. Simulation results illustrate the strengths of the proposed method.

Keywords:Networked control systems, Hybrid systems, Autonomous robots Abstract: A framework for the event-triggered control synthesis under signal temporal logic (STL) tasks is proposed. In our previous work, a continuous-time feedback control law was designed, using the prescribed performance control technique, to satisfy STL tasks. We replace this continuous-time feedback control law by an event-triggered controller. The event-triggering mechanism is based on a maximum triggering interval and on a norm bound on the difference between the value of the current state and the value of the state at the last triggering instance. Simulations of a multi-agent system quantitatively show the efficacy of using an event-triggered controller to reduce communication and computation efforts.

Keywords:Control over communications, Networked control systems, Information theory and control Abstract: As stops and pauses for separating parts of a sentence in language help to convey information, it is also possible to communicate information in communication systems not only by data payload, but also with its timing. We consider an event-triggering strategy that exploits timing information by transmitting in a state-dependent fashion to stabilize a continuous-time, complex, time-invariant, linear system over a digital communication channel with bounded delay and in the presence of bounded system disturbance. For small values of the delay, we show that by exploiting timing information, one can stabilize the system with any positive transmission rate. However, for delay values larger than a critical threshold, the timing information is not enough for stabilization and the sensor needs to increase the transmission rate. Compared to previous work, our results provide a novel encoding-decoding scheme for complex systems, which can be readily applied to diagonalizable multivariate system with complex eigenvalues. Our results are illustrated in numerical simulation of several scenarios.

Keywords:Smart grid, Networked control systems, Linear systems Abstract: We present a framework based on spectral graph theory that captures the interplay among network topology, system inertia, and generator and load damping in determining the overall grid behavior and performance. Specifically, we show that the impact of network topology on a power system can be quantified through the network Laplacian eigenvalues, and such eigenvalues determine the grid robustness against low frequency disturbances. Moreover, we can explicitly decompose the frequency signal along scaled Laplacian eigenvectors when damping-inertia ratios are uniform across buses. The insight revealed by this framework partially explains why load-side participation in frequency regulation not only makes the system respond faster, but also helps lower the system nadir after a disturbance. Finally, by presenting a new controller specifically tailored to suppress high frequency disturbances, we demonstrate that our results can provide useful guidelines in the controller design for load-side primary frequency regulation. This improved controller is simulated on the IEEE 39-bus New England interconnection system to illustrate its robustness against high frequency oscillations compared to both the conventional droop control and a recent controller design.

Keywords:Optimization, Optimization algorithms, Quantized systems Abstract: Data-rich applications in machine-learning and control have motivated an intense research on large-scale optimization. Novel algorithms have been proposed and shown to have order-optimal convergence rates in terms of iteration counts. However, in actual implementations, their performance is severely degraded by the cost of exchanging large gradient vectors between computing nodes. Several lossy gradient compression heuristics have recently been proposed to reduce communications, but few theoretical results exist that quantify how they impact algorithm convergence.

This paper establishes and strengthens the convergence guarantees for gradient descent under a family of gradient compression techniques. For convex optimization problems, we derive admissible step sizes and quantify both the number of iterations and the number of bits that need to be exchanged to reach a target accuracy. Finally, we validate the performance of different gradient compression techniques in simulations. The numerical results highlight the properties of different gradient compression algorithms and confirm that fast convergence with limited information exchange is indeed possible.

Keywords:Optimization algorithms, Networked control systems, Power systems Abstract: In this paper, we develop a class of decentralized algorithms for solving a convex resource allocation optimization problem over a connected network. By observing a connection between the resource allocation and the consensus optimization, we propose a novel class of algorithms for solving the resource allocation problem with improved convergence guarantees. Specifically, we introduce an algorithm for solving the resource allocation problem with an o(1/k) convergence rate when the agents' objective functions are generally convex and per agent local constraints are allowed; we then introduce a gradient-based algorithm for the case when per agent local constraints are absent and show that such scheme achieves geometric convergence with an improved scalability. We also provide a projection-gradient-based algorithm which can handle smooth objective and simple constraints more efficiently.

Keywords:Optimization algorithms, Stochastic optimal control, Distributed control Abstract: We describe a distributed framework for resource sharing problems that we face in communications, microeconomics and various networking applications. In particular, we consider a hierarchical multi-layer decomposition for network utility maximization (NUM), where functionalities are assigned to different layers. The proposed methodology creates solutions having central management and distributed computations. The technique aims to respond to the dynamics of the network by decreasing the communication cost, while shifting more computational load to the edges of the network. The main contribution of this work is the provision of a detailed analysis under the assumption that the network changes are in the same time-scale with the convergence time of the algorithms used for local computations. For this scenario, assuming strong concavity and smoothness of the users’ objective functions, we present convergence rates for each layer.

Keywords:Optimization, Optimization algorithms, Machine learning Abstract: Distributed (federated) learning has become a popular paradigm in recent years. In this scenario private data is stored among several machines (possibly cellular or mobile devices). These machines collaboratively solve a distributed optimization problem, using private data, to learn predictive models. The aggressive use of distributed learning to solve problems involving sensitive data has resulted in privacy concerns. In this paper we present a synchronous distributed stochastic gradient descent based algorithm that introduces privacy via gradient obfuscation in client-server model. We prove the correctness of our algorithm. We also show that obfuscation of gradients via additive and multiplicative perturbations provides privacy to local data against honest-but-curious adversaries.

Keywords:Optimization algorithms, Network analysis and control, Large-scale systems Abstract: This paper addresses the actuator selection problem, i.e., given an interconnection of asymptotically stable linear dynamical systems on a network and m possible actuators choose nu among them to achieve a certain objective. In general, this is a combinatorial optimisation problem which is hard to solve; convex relaxations do not usually yield an optimal solution for the original problem. In this paper we focus on a particular instance of the actuator selection problem, namely the formulation with the trace of the controllability gramian matrix as the optimisation metric, and show that such a choice gives rise to an integer linear program. Using properties of integral polyhedra, we show through a sequence of reformulations that the optimal solution of this problem can be determined by means of a linear program without introducing any relaxation gap. This allows us to obtain the optimal solution using a primal-dual distributed algorithm, thus providing a scalable approach to the problem of actuator placement which has been up to now performed in a centralised manner enumerating all possible placement alternatives. We illustrate the main features of our approach by means of a case study involving a simplified model of the European power grid.

Keywords:Transportation networks, Control of networks Abstract: This paper proposes a logic-based control algorithm for Variable Speed Limits (VSLs) in order to reduce or avoid traffic jams created at bottlenecks. The proposed controller estimates, for each controller time step, the number of vehicles that have to be held back or released by the VSLs in order to maximize the outflow of the bottleneck (avoiding the capacity drop). Afterward, based on the estimated number of vehicles, the VSLs are increased or decreased sequentially. The proposed controller uses a feed-forward structure that allows to anticipate the future evolution of the bottleneck density in order to avoid or reduce trafﬁc breakdowns. As a result, although the implementation of the controller is quite easy with an almost instantaneous computation time, the performance of the controller is effective in reducing Total Time Spent (TTS)

The proposed controller is tested, using the macroscopic traffic flow model METANET, for 10 scenarios and the results are compared with the ones obtained with the Mainstream Traffic Flow Control (MTFC) algorithm, and with the optimal solution. The simulations show that the proposed controller is able to approach the optimal behavior and that its behavior is quite robust (especially comparing with MTFC) in cases where different demands are considered.

Keywords:Transportation networks, Large-scale systems, Estimation Abstract: We address the recent problem of state reconstruction in large scale traffic networks using heterogeneous sensor data. First, we deal with the conditions imposed on the number and location of fixed sensors such that all flows in the network can be uniquely reconstructed. We determine the minimum number of sensors needed to solve the problem given partial information of turning ratios, and then we propose a linear time algorithm for their allocation in a network. Using these results in addition to floating car data, we propose a method to reconstruct all traffic density and flow. Finally, the algorithms are tested in a simulated Manhattan-like network.

Keywords:Transportation networks, Stability of nonlinear systems, Decentralized control Abstract: We study transportation networks controlled by dynamical feedback tolls. We consider a multiscale transportation network model whereby the dynamics of the traffic flows are intertwined with those of the drivers' route choices. The latter are influenced by the congestion status on the whole network as well as dynamic tolls set by the system operator. Our main result shows that a broad class of decentralized congestion-dependent tolls globally stabilise the transportation network around a Wardrop equilibrium. Moreover, using dynamic marginal cost tolls, stability of the transportation network can be guaranteed around the social optimum traffic assignment. This is particularly remarkable as the considered decentralized feedback toll policies do not require any global information about the network structure or the exogenous traffic load on the network or state and can be computed in a fully local way. We also evaluate the performance of these feedback toll policies both in the asymptotic and during the transient regime, through numerical simulations.

Keywords:Traffic control, Smart cities/houses, Transportation networks Abstract: Earlier work has established a decentralized framework to optimally control Connected Automated Vehicles (CAVs) crossing an urban intersection without using explicit traffic signaling while following a strict First-In-First-Out (FIFO) queueing structure. The proposed solution minimizes energy consumption subject to a FIFO-based throughput maximization requirement. In this paper, we extend the solution to account for asymmetric intersections by relaxing the FIFO constraint and including a dynamic resequencing process so as to maximize traffic throughput. To investigate the tradeoff between throughput maximization and energy minimization objectives, we exploit several alternative problem formulations. In addition, the computational complexity of the resequencing process is analyzed and proved to be bounded, which makes the online implementation computationally feasible. The effectiveness of the dynamic resequencing process in terms of throughput maximization is illustrated through simulation.

Keywords:Traffic control, Switched systems Abstract: In this paper, a freeway traffic system regulated with feedback ramp metering controllers is studied. In particular, a switched controller including the proportional-integral feedback regulator PI-ALINEA and a simpler control law is considered as applied to a freeway system. The Asymmetric Cell Transmission Model, properly rewritten as a piecewise affine system switching among different sets of linear difference equations, is the model adopted for representing the system dynamics. The closed-loop stability of this switched system is investigated in the paper and the obtained results are used to properly calibrate the controller gains. These results are then tested and discussed with a simulation analysis reported in the paper.

Keywords:Traffic control, Optimization, Optimization algorithms Abstract: We consider the offset optimization problem that coordinates the offsets of signalized intersections to reduce vehicle queues in large-scale signalized traffic networks. We adopt a recent approach that transforms the offset optimization problem into a complex-valued quadratically-constrained quadratic program (QCQP). Using the special structure of the QCQP, we provide a pi/4-approximation algorithm to find a near-global solution based on the optimal solution of a semidefinite program (SDP) relaxation. Although large-scale SDPs are generally hard to solve, we exploit sparsity structures of traffic networks to propose a numerical algorithm that is able to efficiently solve the SDP relaxation of the offset optimization problem. The developed algorithm relies on a tree decomposition to reformulate the large-scale problem into a reduced-complexity SDP. Under the practical assumption that a real-world traffic network has a bounded treewidth, we show that the complexity of the overall algorithm scales near-linearly with the number of intersections. The results of this work, including the bounded treewidth property, are demonstrated on the Berkeley, Manhattan and Los Angeles networks. From numerical experiments it is observed that the algorithm has a linear empirical time complexity, and the solutions of all cases achieve a near-globally optimal guarantee of more than 0.99.

Keywords:Robust adaptive control, Stochastic systems, Iterative learning control Abstract: In this paper, we present a new architecture for Gaussian Processes Model Reference Adaptive Control (GP-MRAC) trained using a generative network. GP-MRAC is a successful method for achieving global performance in the systems enabling adaptive control. GP-MRAC can handle a broader set of uncertainties without requiring apriori knowledge of the domain of operation. However, existing GP-MRAC work requires estimates of the state-derivate, and this is a primary limitation in the implementation of the controller. In this paper, we alleviate this major limitation by creating Model reference adaptive framework as Generative Network (MRGeN). Our contribution is a generative network architecture for learning Gaussian model to predict system uncertainties without having to estimate the state derivatives while ensuring that the system stability properties are unaffected. We retain the nonparametric nature of the controller by sharing the kernels between GP's and MRGeN, ensuring global performance and stability guarantees. GP-MRGeN can also be viewed as a method of baseline policy transfers, with applications in Reinforcement Learning.

Keywords:Stochastic systems, Systems biology, Network analysis and control Abstract: We develop a robust moment closure for a general class of continuous-time epidemic spreading processes, the elements of which are prevalent in the literature. Our moment closure method takes as input a general stochastic compartmental spreading process defined for n agents and m compartments, and produces a system of 2nm differential equations whose solutions provide nontrivial approximations to the marginal compartmental membership probabilities for each agent. This is an improvement over the commonly used mean-field type approximation, which provides no such guarantee. We demonstrate that our results provide useful predictions with examples performed on two models of competitive spreading processes, and find the developed closure to be more informative than mean-field approximations.

Keywords:Stochastic systems, Lyapunov methods, Filtering Abstract: This paper presents a dual receding horizon output feedback controller for a general non linear stochastic system with imperfect information. The novelty of this controller is that stabilization is treated, inside the optimization problem, as a negative drift constraint on the control that is taken from the theory of stability of Markov chains. The dual effect is then created by maximizing information over the stabilizing controls which makes the global algorithm easier to tune than our previous algorithm. We use a particle filter for state estimation to handle nonlinearities and multimodality. The performance of this method is demonstrated on the challenging problem of terrain aided navigation.

Keywords:Stochastic systems, Aerospace Abstract: We estimate the probability of the first achivement of a given level by a component of a multidimensional process on a given time interval under restrictions on the remaining components. We consider non-Markovian smooth random processes. We specialize our results for a Gaussian process.

Keywords:Stochastic systems, Game theory, Automata Abstract: Cyber-physical systems are conducting increasingly complex tasks, which are often modeled using formal languages such as temporal logic. The system's ability to perform the required tasks can be curtailed by malicious adversaries that mount intelligent attacks. At present, however, synthesis in the presence of such attacks has received limited research attention. In particular, the problem of synthesizing a controller when the required specifications cannot be satisfied completely due to adversarial attacks has not been studied. In this paper, we focus on the minimum violation control synthesis problem under linear temporal logic constraints of a stochastic finite state discrete-time system with the presence of an adversary. A minimum violation control strategy is one that satisfies the most important tasks defined by the user while violating the less important ones. We model the interaction between the controller and adversary using a concurrent Stackelberg game and present a nonlinear programming problem to formulate and solve for the optimal control policy. To reduce the computation effort, we develop a heuristic algorithm that solves the problem efficiently and demonstrate our proposed approach using a numerical case study.

Eindhoven University of Technology, the Netherlands

Keywords:Stochastic systems, Linear systems, Sampled-data control Abstract: We consider a linear control loop with time-varying delays, assumed to be independent and identically distributed random variables following a known probability distribution. We provide Nyquist criteria to assert the convergence to zero of the state statistical moments. The criterion pertaining to the first order moments parallels the one for deterministic time-invariant control loops. In particular, one can determine gain and phase margins. This criterion can be used to assert almost sure stability for positive linear systems. The criterion for the second order moments can be used to assert mean square stability for general linear systems. The applicability of the results is illustrated through a numerical example.

Keywords:Biomedical, Healthcare and medical systems, Adaptive systems Abstract: In this work, we consider the problem of long-term parameter adaptation in artificial pancreas (AP). A parameter adaptation layer that operates on a larger timescale is firstly introduced, on top of the real-time closed-loop glucose control algorithms. A multivariate Bayesian optimization (BO) assisted parameter adaptation framework is then proposed, which features a dynamic parameter selection module that adaptively selects the parameter to be optimized and a BO-based optimization module that adjusts the parameter through optimizing an unknown cost function. The proposed parameter adaptation method is evaluated on the 10-patient cohort of the US Food and Drug Administration accepted Universities of Virginia/Padova simulator through two extreme in silico scenarios. In the first scenario, we show that the proposed method can efficiently reduce average glucose from 173.1 mg/dL to 138.0 mg/dL (p < 0.001) and improve percent time in [70, 180] mg/dL from 63.9% to 93.2% (p < 0.001) without adding any additional risk of hypoglycemia. In the second scenario, the proposed algorithm is able to alleviate hypoglycemia in terms of percent time below 70 mg/dL, from 12.5% to 0.2% (p < 0.001), while improving percent time in [70, 180] mg/dL from 79.4% to 91.4% (p < 0.001). The obtained results indicate feasibility and efficiency of adopting BO-based algorithms in long-term AP adaptation.

Keywords:Biomedical, Predictive control for nonlinear systems, Optimal control Abstract: A single-hormone artificial pancreas (AP) for people with type 1 diabetes consists of a continuous glucose monitor (CGM), a control algorithm, and an insulin pump for administration of fast acting insulin. In this paper, we describe a control algorithm based on nonlinear model pre- dictive control (NMPC) and demonstrate its performance by simulation using an ensemble of virtual patients. The NMPC is based on: 1) a novel formulation of the objective function separating the computed insulin into basal insulin and bolus insulin; 2) a continuous-discrete time model, where continuous stochastic differential equations describe identifiable insulin- glucose dynamics in the body and the observations by the CGM are at discrete times; 3) a nonlinear filtering and prediction algorithm for the continuous-discrete system that is used both offline for identification of the system and online for state estimation; 4) computationally efficient and robust optimization algorithms for the numerical solution of constrained optimal control problems. The algorithm provides insight into the principles for optimal regulation of the glucose concentration for people with type 1 diabetes.

Keywords:Adaptive control, Biomedical, Predictive control for nonlinear systems Abstract: Uncertain delays in the absorption, distribution, and utilization of insulin can cause model inconsistencies and poor glycemic control performance. To address this problem, an adaptive system identification approach able to handle the variable delays in the insulin pharmacokinetics is integrated in this work with a predictive control formulation to explicitly consider the plasma insulin concentration, which facilitates the designed controller to constrain the insulin concentration in the bloodstream. Adaptive models and the estimation of the insulin absorption and utilization rates improve the model predictions and control performance, and the efficacy of the proposed model predictive control algorithm handling the uncertain delays in insulin action is demonstrated using simulation case studies.

Keywords:Biological systems, Machine learning, Pattern recognition and classification Abstract: Blood glucose concentration control is a classic negative feedback problem with insulin secreted by the pancreas as a control variable. Type 1 Diabetes is a chronic metabolic disease caused by a cellular-mediated autoimmune destruction of the pancreas beta-cells, so exogenous insulin administration is needed to regulate the glycaemia. Postprandial glucose regulation is typically based on the knowledge of an estimation of the ingested carbohydrates, of the Carbohydrate-to-insulin ratio, of the correction factor, of the insulin still active and of a measure of the glycaemia just before the meal. Despite the use of this information meal compensation is yet a key unsolved issue. In this paper a new approach based on machine-learning methodologies is proposed to improve postprandial glucose regulation. The proposed approach uses the multiple K-Nearest Neighbors classification algorithm to predict postprandial glucose profile due to the nominal therapy and to suggest a correction to time and/or amount of the meal bolus. This approach has been successfully validated on the adult in silico population of the UVA/PADOVA simulator, which has been accepted by the Food and Drug Administration as a substitute to animal trials.

Keywords:Fault detection, Machine learning, Biomedical Abstract: Subjects affected by Type I Diabetes (T1D) are constantly confronted with the complicated problem of administering themselves an adequate amount of insulin, so as to keep their blood-glucose concentration in a nearly physiological range. Recently, powerful technological tools have been developed to better face this challenge, in particular the so-called Artificial Pancreas (AP). Unluckily, the AP actuator, an insulin pump, is subject to faults, with potential serious consequences for subjects' safety. This calls for the development of advanced fault detection (FD) methods, leveraging the unprecedented data availability in this application. In this paper we tackle the problem of detecting insulin pump malfunctioning using a model-free approach, so that the complex sub-task of identifying a model of patient’s physiology is avoided. Moreover, we employed unsupervised methods since labeled data are hardly available in practice. The adopted data-driven Anomaly Detection (AD) methods are Local Outlier Factor and Connectivity-based Outlier Factor. The methods are applied on a feature set able to account for the physiological dynamics of T1D patients. The proposed algorithms are tested on a synthetic dataset, generated using the "UVA/Padova Type 1 Diabetic Simulator", an accurate nonlinear computer simulator of the T1D subject physiology. Both methods show precision ~75% and recall ~60%. The described approach is suitable both for embedding in medical devices, such as the AP, and implementation in cloud-based remote monitoring systems.

Department of Mathematics and Statistics University of Massachus

Keywords:Biomedical, Healthcare and medical systems, Uncertain systems Abstract: Abstract—Over half a million people in the US suffer from end-stage renal disease (ESRD), and rely on hemodialysis (HD) treatment for survival. The main challenge in HD is the inherent conflict between the need to remove a fixed amount of fluid using ultrafiltration (UF) within a (usually) short amount of time and the fact that high ultrafiltration rates (UFRs) can lead to intradialytic hypotension (IDH). The latter has been associated with an increase in morbidity and mortality. We present a novel approach to design robust UFR profiles to remove a target fluid volume from a HD patient within a prescribed time with minimum UFR levels, while hematocrit satisfies a specific critical hematocrit (HCT) constraint. Our approach is based on fluid dynamics during HD described by a nonlinear fluid volume model comprising intravascular and interstitial pools, whose parameters are given in terms of nominal values with uncertainty ranges. We show that under the designed UFR profile, the HCT of the nonlinear model will meet the critical constraint and the states will remain within a pre-defined region. We demonstrate our results through a simulation using a nonlinear model whose parameters were estimated based on clinical data.

Keywords:Game theory, Optimization, Optimization algorithms Abstract: In this paper we take on the challenge of characterizing the effect of network structure on the economy of public goods by studying a natural model of public facilities with cascading utility. In this game of public facilities, each node of the network is a strategic agent that has the choice to either open a public facility at its location for a certain purchase-cost or take advantage of a public facility opened by another node. It is assumed that using a facility at another node has a cost relative to its distance from the agent. We study the behavior of agents in this game and show that there always exists a pure Nash equilibrium for the game. Moreover, best-response dynamics converges to a pure Nash equilibrium in finitely many steps. We also explore a set of related optimization problems including finding a social optimum for the game and also present a simple algorithm for finding a Nash equilibrium. We then compare the social welfare of the Nash equilibria to that of the social optima using standard game theoretic measures. We show that the price of anarchy is upper-bounded by the diameter of the network and the universal purchase-cost.

Keywords:Game theory, Agents-based systems, Automotive control Abstract: In this paper, we propose a decision making algorithm for autonomous vehicle control at a roundabout intersection. The algorithm is based on a game-theoretic model representing the interactions between the ego vehicle and an opponent vehicle, and adapts to an online estimated driver type of the opponent vehicle. Simulation results are reported.

Keywords:Game theory, Transportation networks, Traffic control Abstract: We study the problem of designing an efficient signaling policy for a traffic manager (TM) when parts of a network experience unpredictable congestion and delays due to external factors, such as accidents or construction that blocks some lanes. To this end, we consider a simple network with two parallel routes, one of which suffers from more unpredictable congestion than the other. In order to understand drivers' behavior, we consider two scenarios - (i) no information from TM and (ii) a binary signal from TM - and assume that a fraction of drivers, called informed drivers, can make use of the TM signal in the latter case and make decisions based on updated information in order to minimize their expected delay.

We show that an optimal signaling policy for TM is a threshold policy: the TM warns the drivers of high congestion if and only if the observed congestion on the route with more unpredictable delays exceeds some threshold. Under a mild condition, this optimal signaling policy is guaranteed to reduce the expected overall network delay. Moreover, we examine how the optimal threshold policy behaves when the congestion delay is either very sensitive or insensitive to traffic and provide a lower bound on the optimal threshold.

Keywords:Game theory, Stability of nonlinear systems, Time-varying systems Abstract: A large population of players has to reach consensus in a distributed way between two options. The two options can be equally favorable or one option can have a higher intrinsic value (asymmetric parameters). In both cases, uncommitted players choose one of the two options depending on the popularity of that option, while committed players can be attracted by those committed to the other option via cross-inhibitory signals. We illustrate the model in different application domains including honeybee swarms, duopolistic competition and opinion dynamics. The main contributions of this paper are as follows: we develop an evolutionary game model to explain the behavioral traits of the honeybees where this model originates; second, we study individuals’ and collective behavior including conditions for local asymptotic stability of the equilibria; third, we study thresholds on the cross-inhibitory signal for the symmetric case and for the corresponding model with heterogeneous connectivity in the case of asymmetric structure with asymmetric parameters; fourth, we study conditions for stability and passivity properties for the collective system under time-varying and uncertain cross-inhibitory parameter in the asymmetric structure and parameters.

Keywords:Game theory, Learning, Agents-based systems Abstract: We use a passivity-based methodology for the analysis and design of reinforcement learning in multi-agent games. We consider an exponentially-discounted reinforcement learning scheme, and show that convergence can be guaranteed for the class of games characterized by the monotonicity property of their (negative) payoff. We further exploit passivity properties to propose a class of higher-order schemes that preserve convergence properties.

Keywords:Game theory, Network analysis and control, Agents-based systems Abstract: In this paper, we propose a control theoretic framework for game problems subject to external disturbances. We consider two cases: the classical setting with full information on the others' decisions, and the partial-decision information setting. The proposed agent dynamics has two components: a gradient-play component and a dynamic internal-model one, which is a reduced-order observer of the disturbance. In the case of partial-information, there is an additional component that drives agents to reach the consensus subspace, where all decision estimates are the same. In both cases, we prove that agents' dynamics converge to the Nash equilibrium, irrespective of the disturbance. Our proofs rely on input-to-state stability properties, under strong monotonicity of the pseudo-gradient and Lipschitz continuity of the extended pseudo-gradient. Simulations are provided to show the usefulness of the algorithm.

Keywords:Machine learning, Optimization Abstract: We consider the outlier detection problem in a linear regression setting. Outlying observations can be detected by large residuals but this approach is not robust to large outliers which tend to shift the residual function. Instead, we propose a new Distributionally Robust Optimization (DRO) method addressing this issue. The robust optimization problem reduces to solving a second-order cone programming problem. We prove several generalization guarantees for our solution under mild conditions. Extensive numerical experiments demonstrate that our approach outperforms Huber's robust regression approach.

Keywords:Machine learning, Intelligent systems, Modeling Abstract: To avoid generating a large number of candidate itemsets during the association rules mining and improve the prediction performance, a new association rule prediction algorithm for classification and regression (ARPACR) is proposed according to the advantages of matrix operation and tree structure. Firstly, the association rules are mined by constructing a new frequent tree. Then, the consequents of the association rules are reconstructed to achieve the classification and regression prediction for new sample. Finally, the experiment results show that it is competitive in prediction accuracy and mining efficiency by comparing with the other algorithms.

Keywords:Machine learning, Optimization algorithms Abstract: Classical results in sparse recovery guarantee the exact reconstruction of s-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since they are based on a worst-case analysis. In this paper, we consider the sparse recovery of signals defined over a graph, for which the dictionary takes the form of an incidence matrix. We derive necessary and sufficient conditions for sparse recovery, which depend on properties of the cycles of the graph that can be checked in polynomial time. We also derive support-dependent conditions for sparse recovery that depend only on the intersection of the cycles of the graph with the support of the signal. Finally, we exploit sparsity properties on the measurements and the structure of incidence matrices to propose a specialized sub-graph-based recovery algorithm that outperforms the standard l_{1}-minimization approach.

Keywords:Machine learning, Pattern recognition and classification, Computational methods Abstract: Ensuring control performance with state and input constraints is facilitated by the understanding of reachable and invariant sets. While exploiting dynamical models have provided many set-based algorithms for constructing these sets, set-based methods typically do not scale well, or rely heavily on model accuracy or structure. In contrast, it is relatively simple to generate state trajectories in a data-driven manner by numerically simulating complex systems from initial conditions sampled from within an admissible state space, even if the underlying dynamics are completely unknown. These samples can then be leveraged for reachable/invariant set estimation via machine learning, although the learning performance is strongly linked to the sampling pattern. In this paper, active learning is employed to intelligently select batches of samples that are most informative and least redundant to previously labeled samples via submodular maximization. Selective sampling reduces the number of numerical simulations required for constructing the invariant set estimator, thereby enhancing scalability to higher-dimensional state spaces. The potential of the proposed framework is illustrated via a numerical example.

Keywords:Machine learning, Networked control systems, Optimal control Abstract: We consider networked control systems consisting of multiple independent controlled subsystems, operating over a shared communication network. Such systems are ubiquitous in cyber-physical systems, Internet of Things, and large-scale industrial systems. In many large-scale settings, the size of the communication network is smaller than the size of the system. In consequence, scheduling issues arise. The main contribution of this paper is to develop a deep reinforcement learning-based control-aware scheduling (DeepCAS) algorithm to tackle these issues. We use the following (optimal) design strategy: First, we synthesize an optimal controller for each subsystem; next, we design a learning algorithm that adapts to the chosen subsystems (plants) and controllers. As a consequence of this adaptation, our algorithm finds a schedule that minimizes the control loss. We present empirical results to show that DeepCAS finds schedules with better performance than periodic ones.

Keywords:Machine learning, Neural networks, Flight control Abstract: Inspired by recent deep learning control research, we develop a sparse and deep neural network architecture and training methodology in order to control a hypersonic flight vehicle with flexible body effects. We leverage a sample-based trajectory training methodology established in our previous work to optimize the weights of the recurrent neural network controller for both performance and robustness. We show that an innovative sparsely-connected control architecture can significantly reduce the computation load on the processor during run-time while improving parameter convergence during optimization. By decomposing the weights of the controller into feed-forward and feed-back elements, we develop a systematic training procedure which further improves optimization results. We demonstrate the effectiveness of the sparse deep learning controller approach through simulation results. Additionally, we explore verifying the robustness metrics of the controller using region of attraction estimation via forward reachable sets.

Keywords:Robotics, Fault detection, Algebraic/geometric methods Abstract: We present a geometric approach for fault detection and isolation (FDI) in robotic manipulators in presence of model uncertainty. A systematic procedure is introduced for representing robotic system model being affine with respect to faults and disturbances. The proposed residual generator has smooth dynamics with freely selectable functions and it does not require high gains or threshold adjustment for the FDI purpose. No assumption on amplitude of faults and their rate is used. The solvability conditions for the FDI problem lead to a quotient observable subspace unaffected by all unknown inputs except the faults. Simulation example demonstrates localization of faults in presence of uncertainty in link moment-of-inertia matrices and measurement noise.

Keywords:Stability of nonlinear systems, Robotics, Optimal control Abstract: In this paper, we present two approaches to obtain graceful transitions between periodic orbits for nonlinear systems with parametrized periodic orbits. In the first approach we consider first a stable family of periodic orbits and show that by slowly varying the parameters, the state trajectory does not deviate far from the family of orbits. We extend this to unstable families of orbits by designing stabilizing controllers. In our second approach, we solve a sequence of tracking problems to obtain the desired graceful transition. Both approaches are illustrated on examples.

Keywords:Robotics, Hybrid systems, Automata Abstract: This paper presents a novel methodology for synthesizing motion tasks with real-time objectives. The methodology utilizes Linear Temporal Logic to define the motion task sequencing. Timed motion objectives are handled by an underlying hybrid automaton that utilizes the concept of Navigation Transformation to provide a time-abstraction of the navigation task. This enables real-time execution of the navigation tasks with analytical guarantees on the safety and the execution time. The resulting system is correct by construction. The performance of the methodology is demonstrated through non-trivial simulations.

Keywords:Robotics, Flexible structures, Modeling Abstract: Soft robots---robots made of soft materials---have strong potential for applications where traditional rigid robots are not suitable (e.g., safely collaborating with humans). However, actuation methods for most existing soft robots still require rigid components to function, and when they do not, they have a limited range of forces and displacements. A new artificial muscle, Twisted-and-Coiled actuators (TCAs), may provide partial solutions to this. They are capable of producing large forces and deformations comparable to or superior to human muscles. However, the dynamic modeling for TCAs when embedded inside soft materials is not trivial due to the coupling of deformations between the actuators and the body. In this paper, we model the dynamics for the thermally driven actuation and extend a dynamic Cosserat rod model to describe the dynamics of the soft body. We also numerically simulate the model to test its correctness. The proposed model is a generalization of existing models and can be applied to the modeling of soft robots when couplings exist between the actuator and the soft body.

Keywords:Robotics, Constrained control, Control applications Abstract: For successful object manipulation with robotic hands, it is important to ensure that the object remains in the grasp at all times. In addition to grasp constraints associated with slipping and singular hand configurations, excessive rolling is an important grasp concern where the contact points roll off of the fingertip surface. Related literature focus only on a subset of grasp constraints, or assume grasp constraint satisfaction without providing guarantees of such a claim. In this paper, we propose a control approach that systematically handles all grasp constraints. The proposed controller ensures that the object does not slip, joints do not exceed joint angle constraints (e.g. reach singular configurations), and the contact points remain in the fingertip workspace. The proposed controller accepts a nominal manipulation control, and ensures the grasping constraints are satisfied to support the assumptions made in the literature. Simulation results validate the proposed approach.

Keywords:Robotics, Human-in-the-loop control, Cooperative control Abstract: This paper is motivated by the control of robot teams by a human. Control challenges arise because i) typically, the team needs to achieve multiple control objectives, shared between the robot team and the human, in order to accomplish a task, ii) robust stability needs to be guaranteed to facilitate the safe interaction with the human and the apriori unknown environment. The concept of passivity has been successfully applied for robust stabilization of robotic systems, however, not in the context of shared control in human-robot team interaction. In this paper we propose a novel control approach which decouples the robot team dynamics into multiple subsystems, each having a different control objective. The proposed control law, suitable for the interaction of the robot team with the human or environment, guarantees passivity of the subsystems. The approach is illustrated in a simulation.

Keywords:Networked control systems, Lyapunov methods, Stability of hybrid systems Abstract: A popular design framework for networked control system (NCSs) is the emulation-based approach combined with hybrid dynamical systems analysis techniques. In the rich literature regarding this framework, various bounds on the maximal allowable transmission interval (MATI) are provided to guarantee stability properties of the NCS using Lyapunov-based arguments for hybrid systems. In this work, we provide a generalization of these Lyapunov-based proofs, showing how the existing results for the MATI can be improved by only considering a different, more general hybrid Lyapunov function, while not altering the conditions in the analysis itself.

Keywords:Networked control systems, Communication networks, Network analysis and control Abstract: This paper presents the formulation and analysis of a fully distributed dynamic event-triggered communication based robust dynamic average consensus algorithm. Dynamic average consensus problem involves a networked set of agents estimating the time-varying average of a dynamic reference signal locally available to individual agents. We propose an asymptotically stable solution to the dynamic average consensus problem what is also robust to network disruptions. Since this robust algorithm requires continuous communication among agents, we introduce a novel dynamic event-triggered communication scheme to reduce the overall inter-agent interactions. It is shown that the event-triggered algorithm is asymptotically stable and free of Zeno behavior. Numerical simulations are provided to illustrate the effectiveness of the proposed algorithm.

Keywords:Networked control systems, Sensor networks, Statistical learning Abstract: This paper considers the problem of designing physical watermark signals to protect a control system against replay attacks. We first introduce the replay attack model, where an adversary replays the previous sensory data in order to fool the controller to believe the system is still operating normally. The physical watermarking scheme, which leverages a random control input as a watermark to detect the replay attack is introduced. The optimal watermark signal design problem is then proposed as an optimization problem, which achieves the optimal trade-off between the control performance and attack detection performance. For the system with unknown parameters, we provide a procedure to asymptotically derive the optimal watermarking signal. Numerical examples are provided to illustrate the effectiveness of the proposed strategy.

Keywords:Networked control systems, Vision-based control, Agents-based systems Abstract: In this paper, we consider the distributed formation control problem for a network of agents using visual measurements. We consider solutions that are bearing based, and agents with double integrator dynamics. We assume that a subset of the agents can track, in addition to their neighbors, a set of static features in the environment. These features are not be considered to be part of the formation to control, but they are used to better control the dynamics of the agents as a whole. In particular, the static features will not provide any constraint on the position of the agents, since they location is, in general, unknown and the formation alone does not specify a relation with them. However, the simple fact that they are static provides enough information to asymptotically control the velocity of the agents.

Keywords:Networked control systems, Linear systems, Optimal control Abstract: We consider an unstable scalar linear stochastic system, X_{n+1}=a X_n + Z_n - U_n, where a geq 1 is the system gain, Z_n's are independent random variables with bounded alpha-th moments, and U_n's are the control actions that are chosen by a controller who receives a single element of a finite set {1, ldots, M} as its only information about system state X_i. We show that M = lfloor arfloor + 1 is necessary and sufficient for beta-moment stability, for any beta < alpha. Our achievable scheme is a uniform quantizer of the zoom-in / zoom-out type. We analyze its performance using probabilistic arguments. We prove a matching converse using information-theoretic techniques. Our results generalize to vector systems, to systems with dependent Gaussian noise, and to the scenario in which a small fraction of transmitted messages is lost.

Keywords:Networked control systems, Stochastic systems, Network analysis and control Abstract: We study the convergence rate of consensus algorithms in a Network of Networks model. In this model, there is a collection of networks, and these individual networks are connected to one another using a small number of links to form a composite graph. We consider a setting where the links between networks are costly to use, and therefore, are used less frequently than links within each network. We model this setting using a stochastic system where, in each iteration, the inter-network links are active with some small probability. Using spectral perturbation theory, we analyze the convergence rate of this system, up to first order in this activation probability. Our analysis shows that the convergence rate is independent of the topologies of the individual graphs; the rate depends only on the number of nodes in each graph and the topology of the connecting edges. We further highlight these theoretical results through numerical examples.

Keywords:Biological systems, Systems biology, Biomolecular systems Abstract: Feedback is both a pillar of control theory and a pervasive principle of nature. For this reason, control-theoretic methods are powerful to analyse the dynamic behaviour of biological systems and mathematically explain their properties, as well as to engineer biological systems so that they perform a specific task by design. This paper illustrates the relevance of control-theoretic methods for biological systems. The first part gives an overview of biological control and of the versatile ways in which cells use feedback. By employing control-theoretic methods, the complexity of interlaced feedback loops in the cell can be revealed and explained, and layered feedback loops can be designed in the cell to induce the desired behaviours, such as oscillations, multi-stability and activity regulation. The second part is mainly devoted to modelling uncertainty in biology and understanding the robustness of biological phenomena due to their inherent structure. Important control-theoretic tools used in systems biology are surveyed. The third part is focused on tools for model discrimination in systems biology. A deeper understanding of molecular pathways and feedback loops, as well as qualitative information on biological networks, can be achieved by studying the "dynamic response phenotypes" that appear in temporal responses. Several applications to the analysis of biological systems are showcased.

Keywords:Biological systems, Systems biology, Biomolecular systems Abstract: In 1939, Walter Cannon wrote in his book The wisdom of the Body : “The living being is an agency of such sort that each disturbing influence induces by itself the calling forth of compensatory activity to neutralize or repair the disturbance”. Since this remarkable statement that postulates the use of feedback control to support life, we have come to appreciate that the use of feedback loops is ubiquitous at every level of biological organization, from the gene to the ecosystem. In this talk, we focus on examples that demonstrate the versatile roles and functions that feedback loops play in cells, and also discuss the need for tools, technologies and mathematical frameworks for studying biological feedback control. In the first part of this talk, we discuss examples of the use for layered feedback loops to produce oscillations and biological rhythms. We describe the use of mathematical tools that led to establishing and analyzing these phenomena. We also discuss the use of feedback in producing multi-stability, with examples illustrating biological switches. In the second part of this talk, we discuss more nuanced use of feedback to modulate quantitatively the activity of biological pathways. We will present examples that include the use of feedback to dynamically shift the dose response of a pathway or to modulate the variability of pathway activity to induce different distributions of behaviors across a population. In the third part of this talk, we discuss available tools for studying and measuring feedback activity in cellular pathways, and illustrate the difficulty inherent in these endeavors. We motivate the need for new tools, both experimental and computational, to study biological feedback. As a closing statement, we will pose the nascent challenge of designing feedback control systems using biomolecules for many biotechnological applications.

Keywords:Biological systems, Systems biology, Biomolecular systems Abstract: The control community has developed many mathematical tools that are tailored to face impor- tant problems in engineering, but can also be successfully adopted to address problems in systems biology: indeed feedback, which is a fundamental concept at the core of control theory, is ubiquitous in biology, at the point that no living being could survive without the myriad of entangled feedback loops that rule its biological functions. When adopting control-theoretic tools for the study of biological problems, there are two fundamental challenges: deal with the huge complexity of biological systems by means of simplifications that allow us to nicely capture the essence of the system and describe it in our framework; convince biologists that such simplifications are worth adopting because, together with non-trivial mathematical tools, they enable a deeper qualitative and quantitative understanding of biological phenomena. The presentation will focus on the simplification of biological models and the use of the mathematical language to solve problems in biology, which can provide a deep insight when supported by an effective communication between mathematicians and biologists. The talk will start with a discussion on mathematical models and uncertainty in biology, focusing on the concept of robust and structural properties, and on system simplifications that exploit special proper- ties (such as monotonicity, or positivity of the impulse response) to combine into a single aggregate element systems composed of many interconnected units (which can be seen as the nodes of a graph). Then, we will overview the principal mathematical tools that are useful in systems biology, ranging from graph theory to differential equations and frequency methods. Several notions will be surveyed, from sophisticated ones, such as degree theory, to more familiar ones, such as Lyapunov theory. Mainstream tools will also be discussed, some of which are inherited from the theory of parametric robustness. The talk will be concluded by showing how the presented tools have been actually applied to the structural analysis of biological systems, including the structural stability of biochemical networks, the structural steady-state influence, and the classification of biological networks based on the analysis of the cycles in the associated graph structure.

Keywords:Biological systems, Systems biology, Biomolecular systems Abstract: One of the central questions in systems and synthetic biology is that of understanding the roles of signal transduction pathways and feedback loops, from the elucidation of such pathways in natural systems to the engineering design of networks that exhibit a desired behavior. This talk discusses certain types of network qualitative information that can be gleaned from “dynamic phenotypes”, a term that we take as encompassing both the transient characteristics of temporal responses and the use of rich classes of probing signals beyond step inputs. We focus on three examples: fold-change detection, non-monotonic responses, and subharmonic oscillations. An ubiquitous property of sensory systems is “adaptation”: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a pro- longed change in their environment. Certain adapting systems, ranging from bacterial chemotaxis pathways to signal transduction mechanisms in eukaryotes, enjoy a remarkable additional feature: scale invariance or “fold change detection” meaning that the initial, transient behavior remains approximately the same even when the background signal level is scaled (“log sensing”). We will review the biological phenomenon, and formulate a theoretical framework leading to a general theorem characterizing scale invariant behavior by equivariant actions on sets of vector fields that satisfy appropriate Lie-algebraic nondegeneracy conditions. The theorem allows one to make experimentally testable predictions, and the presentation will discuss the validation of these predictions using genetically engineered bacteria and microfluidic devices, as well their use as a “dynamical phenotype” for model invalidation. Systems described by order-preserving dynamics are called “monotone systems”. Such systems can be shown to have monotone response properties when starting from steady states: a nondecreasing input can never give rise to a biphasic response, for example. We briefly review some of this theory and show as an example how this tool can be used to invalidate a published model of M. tuberculosis stress response (hypoxic induction pathway). One challenging question in systems biology is that of comparing different architectures for perfect adaptation. For example both incoherent feedforward loops (IFFLs) and integral feedback systems give rise to perfect adaptation and, in some configurations, scale invariance. Recent work has proposed the use of periodic signals to discriminate between these models. We review a theoretical result showing that feedforward loops and monotone systems both lead to entrainment, but nonlinear feedback architectures (such as nonlinear integral feedback) may lead to period doubling bifurcations and even chaos. This result is illustrated through experimental work with C. elegans AIA interneurons, in which odor-evoked intracellular Ca2+ response signatures, to periodic on-off pulses of diacetyl, display subharmonic behavior at high forcing frequencies. The talk will also include some speculative remarks about the role of the shape of transient responses in immune system self/other recognition.

Keywords:Cooperative control, Autonomous systems, Autonomous robots Abstract: This paper presents a set-membership approach for the coordinated control of a fleet of UAVs aiming to search and track an a priori unknown number of targets spread over some delimited geographical area. The originality of the approach lies in the description of the perturbations and measurement uncertainties via bounded sets. A set-membership approach is used to address the localization and tracking problem. At each time step, sets guaranteed to contain the actual state of already localized targets are provided. A set containing the states of targets still to be discovered is also evaluated. These sets are then used to evaluate the control input to apply to the UAVs so as to minimize the estimation uncertainty at the next time step. Simulations considering several UAVs show that the proposed set-membership estimator and the associated control input optimization are able to provide good localization and tracking performance for multiple targets.

Keywords:Cooperative control, Agents-based systems, Observers for nonlinear systems Abstract: The leader-following attitude consensus problem of multiple rigid body systems over switching networks was solved by the distributed observer approach. The resulting control law requires that the control of every rigid body system know the dynamics of the exosystem that produces the desired angular velocity. In this paper, we further consider solving the same problem by the adaptive distributed observer approach. The latter approach is able to provide for each rigid body system the estimation of the dynamics of the exosystem, thus leading to a fully distributed control law for solving the leader-following attitude consensus problem of multiple rigid body systems.

Keywords:Cooperative control, Distributed control, Stability of nonlinear systems Abstract: The Kuramoto model evolves on the circle, i.e. the 1-sphere S^1. A graph G is referred to as S^1-synchronizing if the Kuramoto model on G synchronizes almost globally. This paper generalizes the Kuramoto model and the concept of synchronizing graphs to the Stiefel manifold St(p,n). Previous work on generalizations of the Kuramoto model have largely been influenced by results and techniques that pertain to the original model. It was recently shown that all connected graphs are S^n-synchronizing for all n>=2. However, that does not hold for n=1. Previous results on generalized models may thus have been overly conservative. The n-sphere is a special case of the Stiefel manifold, namely St(1,n+1). As such, it is natural to ask for the extent to which the results on S^n can be extended to the Stiefel manifold. This paper shows that all connected graphs are St(p,n)-synchronizing provided the pair (p,n) satisfies p=<2n/3-1.

School of Aerospace Engineering, Xiamen University

Keywords:Cooperative control, Modeling, Computational methods Abstract: The affine formation maneuver control problem of leader-follower linear multi-agent systems with undirected interaction graphs is studied in this paper. First, this paper provides and proves the sufficient and necessary conditions for affine localizability. If given a d-dimensional nominal formation with no fewer than d+1 leaders and generic universal rigidity,then any formation shape satisfying affine transformation can be obtained in arbitrary dimension only by these leaders. In the sequel, a novel distributed control method for the followers with linear dynamic models is designed to achieve the desired time-varying maneuvers, and the global stability is proved.Simulations are carried out to verify the theoretical results,which show that these followers can track the time-varying references continuously and accurately.

Keywords:Cooperative control, Agents-based systems, Optimal control Abstract: We present an optimal cooperative control method for a distance-based, leader-following formation control of multi-agent systems with energy constraints. In order to develop distributed control algorithms, we introduce a local rigidity matrix. We combine the rigidity theory and State-Dependent Riccati Equation (SDRE) method to develop a formation control scheme. The proposed method asymptotically minimizes a weighted cost function that includes formation cost and energy consumption for a given mission. The leader agent is aware of the desired trajectory and the followers measure relative distances of their neighbors only. We choose the weighting factors of the cost function to be dependent on the energy level of the agents. The proposed method guarantees the local asymptotic stability of the system. Moreover, we offer a solution for the global asymptotic stability of the closed-loop system. Simulation results illustrate the effectiveness of the proposed method in two- and three-dimensional spaces.

Keywords:Distributed parameter systems Abstract: We tackle the boundary control problem for a class of viscous Hamilton-Jacobi PDEs, considering bilateral actuation, i.e., at the two boundaries of a 1-D spatial domain. First, we solve the nonlinear trajectory generation problem for this type of PDEs, providing the necessary feedforward actions at both boundaries. Second, in order to guarantee trajectory tracking with an arbitrary decay rate, we construct nonlinear, full-state feedback laws employed at the two boundary ends. All of our designs are explicit since they are constructed interlacing a feedback linearizing transformation (which we introduce) with backstepping. Due to the fact that the linearizing transformation is locally invertible, only regional stability results are established, which are, nevertheless, accompanied with region of attraction estimates. Our stability proofs are based on the utilization of the linearizing transformation together with the employment of backstepping transformations, suitably formulated to handle the case of bilateral actuation. We illustrate the developed methodologies via application to traffic flow control and we present consistent simulation results.

Keywords:Distributed parameter systems, Stability of linear systems, Flexible structures Abstract: We consider coupled systems consisting of a well-posed and impedance passive linear system (that may be infinite dimensional), with semigroup generator A and transfer function GGG, and an internal model controller (IMC), connected in feedback. The IMC is finite dimensional, minimal and impedance passive, and it is tuned to a finite set of known disturbance frequencies o_j, where jin{1, ldots n}, which means that its transfer function gggg has poles at the points io_j. We also assume that gggg has a feedthrough term d with Re d>0. We assume that ReGGG(io_j)>0 for all jin{1,ldots n} and the points io_j are not eigenvalues of A. We can show that the closed-loop system is well-posed and input-output stable (in particular, (I+ggggGGG)^{-1}in H^infty and also GGG(I+ggggGGG)^{-1}in H^infty). It is also easily seen that the closed-loop system is impedance passive. We show that if A has at most a countable set of imaginary eigenvalues, that are all observable, and A has no other imaginary spectrum, then the closed-loop system is strongly stable. This result is illustrated with a wind turbine tower model controlled by an IMC.

Keywords:Distributed parameter systems, Optimal control, Process Control Abstract: Model predictive control is developed for the example of a boundary controlled linear diffusion-convection-reaction system by exploiting the flatness property of the PDE. This enables us to formulate the optimal control problem in terms of the flat output and its successive time derivatives, which are imposed by means of an integrator chain. By taking into account the flatness-based state and input parametrizations constraints on the PDE state and input can be easily integrated into the approach. The method is illustrated for different simulation scenarios involving an observer to estimate the states of the integrator chain from the PDE solution.

Keywords:Optimization, Delay systems, Stochastic systems Abstract: We present a Newton-based extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of time delays. Different from previous works about extremum seeking for higher derivatives, we employ stochastic instead of periodic perturbations, allow arbitrarily long output delays as well as dynamic maps. We incorporate a predictor feedback with a perturbation-based estimate for the Hessian's inverse using a differential Riccati equation and stochastic demodulation signals making the convergence rate user-assignable. Furthermore, exponential stability and convergence to a small neighborhood of the unknown extremum point is achieved for locally quadratic derivatives by using a backstepping transformation and averaging theory in infinite dimensions for stochastic systems. We also present simulations to highlight the effectiveness of our predictor-feedback scheme.

Keywords:Distributed parameter systems, Sampled-data control, Observers for Linear systems Abstract: The existing sampled-data observers for 2D heat equations use spatially averaged measurements, i.e., the state values averaged over subdomains covering the entire space domain. In this paper, we introduce an observer for a 2D heat equation that uses pointlike measurements, which are modeled as the state values averaged over small subsets that do not cover the space domain. The key result, allowing for an efficient analysis of such an observer, is a new inequality that bounds the L2-norm of the difference between the state and its point value by the reciprocally convex combination of the L2-norms of the first and second order space derivatives of the state. The convergence conditions are formulated in terms of linear matrix inequalities feasible for large enough observer gain and number of pointlike sensors. The results are extended to solve the H-infinity filtering problem under continuous and sampled in time pointlike measurements.

Keywords:Distributed parameter systems, Stability of linear systems, LMIs Abstract: We present a framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet, Neuman and mixed boundary conditions. The results in this paper apply to systems with a single spatial variable and assume existence and continuity of solutions except in such cases when existence and continuity can be inferred from existence of a Lyapunov function. Our approach is based on a new concept of state for PDE systems which allows us to express the derivative of the Lyapunov function as a Linear Operator Inequality directly on L_2 and allows for any type of suitably well-posed boundary conditions. This approach obviates the need for integration by parts, spacing functions or similar mathematical encumbrances. The resulting algorithms are implemented in Matlab, tested on several motivating examples, and the codes have been posted online. Numerical testing indicates the approach has little or no conservatism for a large class of systems and can analyze systems of up to 20 coupled PDEs.

Keywords:Observers for nonlinear systems, Hybrid systems, Mechatronics Abstract: We propose a hybrid nonlinear high-gain observer to estimate the speed of rotary systems equipped with potentiometer-based, capacitive or hall-effect rotary sensors or providing angular measurements evolving in S1, exhibiting unpredictable jumps of 2 pi. A hybrid measurement model is proposed, based on which a hybrid high-gain observer is synthesized, which does not require the knowledge of the jump times. Asymptotic tracking of the proposed observer is proven. A sampled-data approximation of the proposed observer is developed as well, based on which an experimental validation shows suitability for real-time applications.

Keywords:Observers for nonlinear systems Abstract: This paper proposes an observer for generating depth maps of a scene from a sequence of measurements acquired by a two-plane light-field (plenoptic) camera. The observer is based on a gradient-descent methodology. The use of motion allows for estimation of depth maps where the scene contains insufficient texture for static estimation methods to work. A rigourous analysis of stability of the observer error is provided, and the observer is tested in simulation, demonstrating convergence behaviour.

Keywords:Observers for nonlinear systems, Output regulation Abstract: Homographies provide a robust and reliable cue for visual servo control of robots. Some nonlinear observers have been recently developed for the estimation of temporal sequences of homographies associated with rigid-body motion of a camera observing a stationary planar scene. However, these algorithms do not model well time-varying changes in the homography velocity and tend to perform poorly when the camera or the scene moves fast. In this paper, an internal model-based observer posed on SL(3) for homography estimation is proposed allowing for dealing with complex camera-scene trajectories such as circular and sinusoidal motions of the camera and/or the scene. Rigorous proof of local asymptotic stability is established and excellent performance of the proposed observer is justified by experiments using an IMU-Camera prototype observing an oscillating planar target.

Keywords:Observers for nonlinear systems, Fault detection, LMIs Abstract: We address the problem of robust state estimation and attack isolation for a class of discrete-time nonlinear systems with positive-slope nonlinearities under (potentially unbounded) sensor attacks and measurement noise. We consider the case when a subset of sensors is subject to additive false data injection attacks. Using a bank of circle-criterion observers, each observer leading to an Input-to-State Stable (ISS) estimation error, we propose a estimator that provides robust estimates of the system state in spite of sensor attacks and measurement noise; and an algorithm for detecting and isolating sensor attacks. Our results make use of the ISS property of the observers to check whether the trajectories of observers are “consistent” with the attack-free trajectories of the system. Simulations results are presented to illustrate the performance of the results.

Keywords:Observers for nonlinear systems, Lyapunov methods, Estimation Abstract: In this paper a novel method is proposed for state estimation of nonlinear systems using high-gain observers (HGOs) and adaptive techniques. In this regard, Multiple HGOs (MHGO) are run simultaneously, and the information obtained from individual observers are combined adaptively. To be able to suitably combine the state estimations, it is first proved that there exist some constant coefficients that provide the perfect estimation. Then, the RLS algorithm is employed to find those coefficients. The convergence of the state estimations to the system states is guaranteed, and it is shown that the MHGO is able to attenuate the inherent peaking phenomenon in HGOs. Finally, the simulation results are presented which show the superiority of the proposed MHGO method in state estimation and improving the transient response.

Keywords:Observers for nonlinear systems, Aerospace, Robotics Abstract: This paper presents an asymptotically-convergent nonlinear attitude estimator for rigid bodies using a rate gyro and GPS. Double-difference carrier phase measurement are provided by at least two GPS antennas. The unknown integer ambiguity factor related to GPS carrier phase measurement is estimated along with the attitude. An observability condition is derived to guarantee convergence of the estimator when a single baseline vector is available with more than four satellites in view. Finally, experimental test from a survey boat illustrates performance of the proposed observer.

Keywords:Adaptive control, Adaptive systems, Linear parameter-varying systems Abstract: Even though the raison d'etre of adaptive control is to cope with time-varying environments, for the sake of mathematical tractability researchers have traditionally confined their attention to time-invariant (or slowly time-varying) systems. The limitations of classical adaptive control, however, become evident when the controllers are called upon to respond to rapidly varying environments. In recent years numerous non-technical applications such as medical emergencies, trading on the stock market, conflict management using counter terrorism measures, and technical applications such as aircraft and automobile control, energy management, and manufacturing are arising which call for fast and accurate control in such environments.

One of the main difficulties while dealing with time-varying environment is in characterizing them appropriately, so that the problems posed lend themselves to mathematical analysis. In this paper we attempt to combine multiple fixed and adaptive models in a hierarchical approach to achieve fast and accurate response, when the parameters of a plant vary periodically in an unknown fashion. Theoretical analyses followed by simulation studies of increasingly complex static and dynamical systems with single and multiple parameters are presented. Many of the theoretical questions addressed in this paper in the specific context of systems with periodic parameters are found to be relevant for adaptation in more general time-varying environments.

Keywords:Control system architecture, Adaptive control, Uncertain systems Abstract: In this paper, an adaptive control architecture is proposed for uncertain dynamical systems subject to interconnected actuated and unactuated dynamics with performance guarantees enforced on both dynamics. Specifically, the control and performance enforcement of the unactuated dynamics is accomplished through the physical interconnection with the actuated dynamics, where the proposed control is applied to stabilize the overall interconnected system in the presence of unknown physical interconnections as well as uncertainties in both the actuated and unactuated dynamics. The performance guarantees are enforced using a set-theoretic model reference adaptive control approach such that the respective system error trajectories of the actuated and unactuated dynamics are restricted to stay inside user-defined compact sets. We then use linear matrix inequality to verify stability of suitable control parameters as well as the allowable system uncertainties and unknown physical interconnections.

Keywords:Adaptive control, Flight control, Control applications Abstract: An adaptive longitudinal control law for moving mass control of a novel flight vehicle configuration is proposed. The coupling dynamic model between angle of attack and deflection of moving mass is generated. The dynamic analysis indicates that the proposed moving mass configuration with larger mass ratio gives rise to more dynamic coupling and maneuverability. Moreover, the control authority is determined by the mass ratio of the moving mass and the difference between the mass center of the moving mass and the mass center of the vehicle body. To deal with the coupling caused by the additional inertia moment of moving mass, the coupling dynamics system is transformed into a cascade system for controller design. Active disturbance rejection control framework is employed to design the adaptive longitudinal controller. Its extended state observer estimates the total disturbance to overcome the uncertainties in the flight vehicle model. The simulation results show that the proposed configuration is feasible and validate the quality of the adaptive controller which ensures good performance.

Keywords:Adaptive systems, Distributed control, Smart cities/houses Abstract: Self-stabilizing information spreading algorithms are an important building block of many distributed systems featuring in aggregate computing. The convergence dynamics of self-stabilizing information spreading, however, have not previously been characterized, except in the special case of a distance finding variant known as the Adaptive Bellman-Ford (ABF) Algorithm. As a step towards understanding the behavior of these algorithms, particularly when interconnected with other building blocks, it is important to develop a framework to demonstrate their robust stability. Accordingly, this paper analyzes an extremely general information spreading algorithm of which ABF is a special case. We provide a proof of global uniform asymptotic stability, upper bound on the time to converge, and ultimate bounds on state error in face of persistent perturbations.

Keywords:Adaptive control, Predictive control for linear systems, Output regulation Abstract: In this paper, almost strictly positive real (ASPR) based adaptive output feedback control with an output predictive control as a feedforward input is proposed for linear continuous-time systems. The method can design a stable and simple output predictive control based adaptive controller with higher control performance for uncertain systems. The method for discrete-time systems with two-degree-of-freedom control structure is expanded to continuous-time systems and the stability of the obtained control system will be analyzed in this paper. The effectiveness of the proposed method is confirmed through numerical simulations for simple second order uncertain system.

Keywords:Adaptive control, Agents-based systems, Stability of nonlinear systems Abstract: In this paper, a performance guaranteed control algorithm is presented for the consensus control of a class of unknown nonlinear multi-agent systems (MASs) with unknown control directions. It is shown that the states of agents stay within prescribed time-varying restrictions for all time. To attain these new results, an equivalent unconstrained MAS is generated from the original constrained one via a state transformation technique. Stabilization and consensus of the transformed agent states ensure both the consensus of the original agent states as well as the satisfaction of the prescribed restrictions. Based on the Nussbaum gain technique, the unknown control direction problem is solved. Consensus task is achieved theoretically via using Lyapunov synthesis, along with all the closed-loop signals being bounded. Additionally, in the proposed control design, each agent only exchanges the information with its neighbours. Hence, the proposed consensus protocol is distributed. Finally, simulation results demonstrate the effectiveness of the developed controller.

Keywords:Identification, Kalman filtering, Observers for nonlinear systems Abstract: This paper proposes a globally exponentially stable (GES) discrete-time observer for estimating the constant unknown parameters describing a single biased continuous time sinusoidal signal. A discrete-time dynamic system is derived based on the sampled output that is key to the design of the estimation solution. The observability properties of this system are analyzed and a filter design is proposed which guarantees that the estimation error converges globally exponentially fast to zero. Realistic simulation results are presented, in the presence of measurement noise, that illustrate the performance of the proposed solutions.

Keywords:Identification, Nonlinear systems identification, Stochastic systems Abstract: We analyze the statistical performance of identification of stochastic dynamical systems with non-linear measurement sensors. This includes stochastic Wiener systems, with linear dynamics, process noise and measured by a non-linear sensor with additive measurement noise. There are many possible system identification methods for such systems, including the Maximum Likelihood (ML) method and the Prediction Error Method (PEM). The focus has mostly been on algorithms and implementation, and less is known about the statistical performance and the corresponding Cramer-Rao Lower Bound (CRLB) for identification of such non-linear systems. We derive expressions for the CRLB and the asymptotic normalized covariance matrix for certain Gaussian approximations of Wiener systems to show how a non-linear sensor affects the accuracy compared to a corresponding linear sensor. The key idea is to take second order statistics into account by using a common parametrization of the mean and the variance of the output process. This analysis also leads to a ML motivated identification method based on the conditional mean predictor and a Gaussian distribution approximation. The analysis is supported by numerical simulations.

Keywords:Identification, Estimation, Identification for control Abstract: The indirect approach to continuous-time system identification consists in estimating continuous-time models by first determining an appropriate discrete-time model. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree 1, independent of the relative degree of the strictly proper real system. In this paper, a refinement of these methods is developed. Inspired by indirect PEM, we propose a method that enforces a fixed relative degree in the continuous-time transfer function estimate, and show that the resulting estimator is consistent and asymptotically efficient. Extensive numerical simulations are put forward to show the performance of this estimator when contrasted with other indirect and direct methods for continuous-time system identification.

Keywords:Identification, Estimation, Linear systems Abstract: This paper studies the asymptotic properties of the hyperparameter estimators including the leave-k-out cross validation (LKOCV) and r-fold cross validation (RFCV), and discloses their relation with the Stein's unbiased risk estimators (SURE) as well as the mean squared error (MSE). It is shown that as the number of data goes to infinity, both the LKOCV and RFCV share the same asymptotic best hyperparameter minimizing the MSE estimator as the SURE does if the input is bounded and the ratio between the training data and the whole data tends to zero. We illustrate the efficacy of the theoretical result by Monte Carlo simulations.

Keywords:Identification, Estimation, Time-varying systems Abstract: The paper deals with the estimation of characteristics of the state and measurement noises of a system described by the linear time-varying state space model, where the state and measurement noises can be either mutually correlated or correlated in time. In particular, a novel correlation measurement difference method is designed. The method, which may provide unbiased estimates, is based on a statistical analysis of the prediction error of an augment measurement vector leading into a system of linear equations. The theoretical results are thoroughly discussed and illustrated in numerical examples.

Keywords:Identification, Machine learning Abstract: This paper proposes a new kernel-based system identification method which uses a priori knowledge on the DC gain (i.e., the steady state response to the unit step input) of the system in addition to the prior on the impulse response. It is not easy to encode the prior on the DC gain to prior distributions for the impulse response estimation. This paper proposes a new method which first estimates the step response and then constructs the impulse response model of the system. In particular, we divide the step response into the steady state response and its residuals, and design a prior distribution for them based on a priori knowledge on the system. The effectiveness of the proposed method is verified by detailed numerical examples from the perspectives of estimation accuracy for both the impulse response and the step response.

Keywords:Estimation, Observers for nonlinear systems, Automotive systems Abstract: Electrochemical sensors have been widely applied in various industries for monitoring and feedback control of air quality. However, many of the existing electrochemical sensors are cross-sensitive to interfering gases while measuring the target gases. In this study, we proposed a direct algebraic approach-based decomposition algorithm suitable for a class of nonlinear dynamic systems with cross-sensitive output measurements for state and output estimations. Nonlinear system state and output estimations, based on cross-sensitive output measurement, are rather challenging due to the surjective mapping from system states to direct output reading. The proposed algorithm utilizes the cross-sensitive output measurement and its time derivative information to systematically solve for the actual system states or outputs. The proposed algorithm was applied to the urea-based SCR system where the outlet NOx sensor suffers an ammonia cross-sensitivity issue while measuring NOx emissions. Simulation results over transient US06 cycle verified the effectiveness of the proposed decomposition algorithm in decoupling NOx concentrations and NH3 concentrations from the cross-sensitive NOx sensor readings, as well as in estimating the ammonia coverage ratio. The proposed decomposition algorithm can potentially be applied to a broad class of nonlinear dynamic systems with cross-sensitive electrochemical sensors to improve the system performance.

Keywords:Estimation Abstract: This paper proposes a distributed set-membership approach based on zonotopes for interconnected systems with coupled states and unknown-but-bounded uncertainties (both state disturbances and measurement noise). The objective of the distributed set-membership approach is to find a sequence of distributed zonotopes to bound uncertain states of each subsystem (called agent) instead of making use of a single zonotope to bound all the uncertain states. In the proposed approach, these distributed state bounding zonotopes are only corrected by their own measurement outputs. To predict the state at the next sampling time, each agent sends its own state-bounding zonotope to its neighbors. For achieving robust state estimation, we propose a novel optimization problem based on the P-radius minimization criterion. Finally, the effectiveness of the proposed approach is provided with a numerical example.

Keywords:Closed-loop identification, Subspace methods, Estimation Abstract: The stability margin and the gap metric are powerful tools for closed-loop robust stability analysis in control system designs. In order to develop a data-driven framework for the real-time evaluation of the closed-loop stability, this paper presents a study on data-driven estimation of the closed-loop stability margin using time domain measurements. The core of the study is to find an estimation of the multiplication operator of the closed-loop transfer function matrices, where a data-driven stable image representation (SIR) of the system is identified using closed-loop data sets based on the orthogonal projection technique. The contributions of this paper efficiently bridge the gap between robustness analysis/design and data-driven techniques for the future research. The main results of this paper are verified and demonstrated through randomly generated systems and designed closed-loops.

Keywords:Estimation, Observers for nonlinear systems, Uncertain systems Abstract: This paper presents an efficient recursive algorithm for computing tight enclosures of the set of states consistent with a given nonlinear discrete-time model, an observed output sequence, and given bounds on disturbances and measurement errors. This is commonly called set-based state estimation, and has applications in verification, fault detection, and robust control. The presented algorithm is based on the theory of differential inequalities (DI), which has been extensively developed for nonlinear reachability analysis. Contemporary DI methods make use of redundant model equations to achieve tight reachability bounds at low cost. Here, we extend these methods to set-based state estimation and show very favorable results relative to other recursive algorithms in common use. Notably, however, this approach is only applicable to forward-Euler-discretized systems satisfying a step size bound.

Keywords:Linear parameter-varying systems, Nonlinear systems identification, Estimation Abstract: This note explains the advantage of employing integral system representations of linear systems in application to state and input estimation for a broad class of LPV systems. Integral (kernel) representations of linear systems are seen as vehicles for retaining local information about the system's input-output behaviour in which the notion of initial or boundary conditions play no role. An important by-product of kernel system representations is their capacity for reconstruction of time derivatives of the measured system output by using the kernel derivatives. These attributes immediately lead to the construction of kernel-based dead-beat state and parameter estimators for linear systems. The approach is extended here to LPV systems with measured scheduling parameters, or else LPV systems in which the scheduling parameters cannot be measured directly, but whose values may be inferred from the output observations of other, possibly nonlinear, dynamical systems. It is shown that the lack of knowledge of the system input does not prejudice successful state estimation provided that the system has strong observability properties that effectively permit input reconstruction in a suitable B-spline basis. The method also applies to nonlinear smooth systems that can be transformed to LPV systems with dynamically varying parameters. An example of a strongly nonlinear system is presented for which the extended Kalman filter is known to fail.

Keywords:Estimation Abstract: We present a general and computationally tractable method for the operation of a Backwards Information Filter on a linear Gaussian Mixture Model system, which can be used to generate the smoothed density. Unlike other methods, the algorithm proposed here does not make unimodal approximations, and is exact with the exception of the mode reduction strategy.

Keywords:Lyapunov methods, Decentralized control, Large-scale systems Abstract: We prove a small-gain theorem which addresses the problem of global uniform finite-time stability of infinite networks. The network is composed of a countable set of finite-dimensional subsystems of ordinary differential equations, each of which is interconnected with a finite number of its ``neighbors'' only and is assumed to be finite-time input-to-state stable with respect to its finite-dimensional inputs produced by this finite set of the neighbors. As a corollary we obtain a new result on decentralized finite-time stabilization of infinite networks composed of a countable set of strict-feedback form systems of ordinary differential equations. For this, we combine our new small-gain theorem with the method proposed by S. Pavlichkov and C.K. Pang (NOLCOS-2016) for the gain assignment of the strict-feedback form systems in the case of finite networks. The current results address the finite-time stability and finite-time stabilization and redesign the technique proposed in recent work by S. Dashkovskiy and S. Pavlichkov (IFAC World Congress-2017) for asymptotic stabilization of infinite networks.

Keywords:Lyapunov methods, Stability of nonlinear systems, Robust control Abstract: This article presents a theoretical framework to study finite-time and fixed-time input-to-state stability of nonlinear systems using the implicit Lyapunov function formulation. This approach allows to determine stability, robustness and convergence type of a given system without relying in an explicit Lyapunov function.

Keywords:Lyapunov methods, Time-varying systems, Autonomous robots Abstract: This study deals with a design method of a time-varying control Lyapunov function for nonlinear systems defined on manifolds. We introduce herein a definition of a time-varying control Lyapunov function (time-varying CLF) defined on manifolds, which is a natural extension of the CLF defined on Euclidean space. We also propose a time-varying CLF design method by extending a conventional CLF design method, called the minimum projection method. We demonstrate the effectiveness of the proposed method by an application, namely the dynamical obstacle avoidance control problem. As a result, we can design an analytic global controller for dynamical obstacle avoidance of a mobile robot.

Keywords:Lyapunov methods, Stability of nonlinear systems Abstract: Lyapunov functions and control Lyaupunov functions are a well established tool in the analysis of stability properties of dynamical systems as well as in the design of stabilizing feedback controllers. In order to address problems such as stabilization in the presence of unsafe sets of states or obstacle avoidance, one potential approach involves rendering such obstacles unstable by feedback. To this end we introduce (nonsmooth) Chetaev and control Chetaev functions and demonstrate their sufficiency for complete instability properties of dynamical systems. While a "time-reversal" approach is frequently used to study instability in reverse time of an asymptotically stable point in forward time, we demonstrate via an example that such an approach cannot be used to generate Chetaev functions from nonsmooth Lyapunov functions via a simple change of sign in the time argument.

Keywords:Uncertain systems, Lyapunov methods, Stability of nonlinear systems Abstract: This paper aims to compute the region of attraction (ROA) of equilibrium points whose location is modified by the uncertainties. The local stability region is formulated as an equilibrium-independent level set by restricting the attention to contractive functions which do not explicitly depend on the equilibrium. Another favourable feature of the approach is that it can be applied to systems having one or more branches of steady-state solutions (e.g. multistable systems). Inner estimates of the ROA are numerically computed by means of Sum of Square techniques, which allow to specify the allowed uncertainty range and the analyzed branch as set containment conditions, resulting in a compact and flexible formulation. A numerical example shows the application of the method and highlights its peculiar features.

Keywords:Lyapunov methods, Output regulation, Stability of nonlinear systems Abstract: A maneuver regulation controller for reduced gravity vertical flight is developed using intuition based on an internal model of the quadratically increasing (in time) aerodynamic drag. This leads to a controller employing a chain of three integrators. Since the drag ``disturbance'' actually results from a nonlinear feedback, the usual linear stability analysis is insufficient. The proper framework is found using a transverse coordinate system about the desired maneuver, where one may show that the maneuver is in fact exponentially attractive. Experimental performance of the resulting control system are also presented.

Keywords:Hybrid systems, Stability of hybrid systems, PID control Abstract: In this paper, we propose a modeling and design technique for a proportional-integral-derivative (PID) controller in the presence of aperiodic intermittent sensor measurements. Using classical control design methods, PID controllers can be designed when measurements are available periodically, at discrete time instances, or continuously. Unfortunately, such design do not apply when measurements are available intermittently. Using the hybrid inclusions framework, we model the continuous-time plant to control, the mechanism triggering intermittent measurements, and a hybrid PID control law defining a hybrid closed-loop system. We provide sufficient conditions for uniform global asymptotic stability using Lyapunov stability methods for sets. These sufficient conditions are used for the design of the gains in the hybrid PID controller. Also, we propose relaxed sufficient conditions so as to provide a computationally tractable design method leveraging a polytopic embedding approach. The results are illustrated via numerical examples.

Keywords:Hybrid systems Abstract: We introduce a holistic framework for the analysis, approximation and control of the trajectories of hybrid dynamical systems which display event-triggered discrete jumps in the continuous state. We begin by demonstrating how to explicitly represent the dynamics of this class of systems using a single piecewise-smooth vector field defined on a manifold, and then employ Filippov's solution concept to describe the trajectories of the system. The resulting hybrid Filippov solutions greatly simplify the mathematical description of hybrid trajectories, providing a unifying solution concept with which to work and giving new insight into pathologies such as the Zeno phenomena. Extending previous efforts to regularize piecewise-smooth vector fields, we then introduce a family of smooth control systems whose flows are used to approximate the hybrid Filippov solution in the numerical setting. The two solution concepts are shown to agree in the limit, under mild regularity conditions.

Keywords:Behavioural systems, Hybrid systems, Modeling Abstract: In this paper, we describe a method for representing a behavioral dynamical system as a Generalized Synchronization Tree (GST). The method of representation we propose is analogous to the ``unrolling'' of a Labeled Transition System (LTS) into a bisimilar Synchronization Tree (ST). Thus, for behavioral systems endowed with state maps, we are able to establish conditions under which bisimilar behavioral systems result in bisimilar GST representations and conversely. Preservation of bisimulation equivalence is critical to future study of composition operators for behavioral systems and GSTs. Additionally, we define a composition operator for GSTs constructed from behavioral systems, and prove a congruence result for strong bisimulation.

Keywords:Hybrid systems Abstract: This paper proposes barrier functions for the study of forward invariance in hybrid systems modeled by hybrid inclusions. After introducing an appropriate notion of a barrier function, we propose sufficient conditions to guarantee forward invariance properties of a set for hybrid systems with nonuniqueness of solutions, solutions terminating prematurely, and Zeno solutions. Our conditions involve infinitesimal conditions on the barrier certificate and Minkowski functionals. Examples illustrate the results.

Keywords:Hybrid systems, Constrained control Abstract: Real-life control systems are hierarchies of interacting layers; often consisting of a planning layer, a trajectory generation layer, and a trajectory-following layer. Independently designing the layers without taking the interactions between layers into account makes it difficult to obtain safety guarantees when executing a high-level plan. In this paper we combine ideas from safety-critical control and high-level policy synthesis to develop a principled connection between a high-level planner in a low-dimensional space, and a low-level safety-critical controller acting in the full state space. We introduce a new type of simulation relation and show that barrier functions can be used to abstract a high-dimensional system via the relation. As a result, we obtain provably correct execution of high-level policies by low-level optimization-based controllers. The results are demonstrated with a quadrotor surveillance example.

Keywords:Hybrid systems, Sampled-data control, Quantized systems Abstract: This paper deals with the synthesis of symbolic controllers for interconnected sampled-data systems where each component has its own sampling period. A compositional approach based on continuous-time assume-guarantee contracts is used. We provide sufficient conditions guaranteeing for a sampled-data system, satisfaction of an assume-guarantee contract and completeness of trajectories. Then, compositional results can be used to reason about interconnection of multiperiodic sampled-data systems. We then show how discrete abstractions and symbolic control techniques can be applied to enforce the satisfaction of contracts and ensure completeness of trajectories. Finally, theoretical results are applied to a vehicle platooning problem on a circular road, which show the effectiveness of our approach.

Keywords:Power systems, Uncertain systems, Optimization Abstract: This paper addresses a multi-stage generation investment problem for a strategic (price-maker) power producer in electricity markets. This problem is exposed to different sources of uncertainty, including short-term operational (e.g., rivals' offering strategies) and long-term macro (e.g., demand growth) uncertainties. This problem is formulated as a stochastic bilevel optimization problem, which eventually recasts as a large-scale stochastic mixed-integer linear programming (MILP) problem with limited computational tractability. To cope with computational issues, we propose a consensus version of alternating direction method of multipliers (ADMM), which decomposes the original problem by both short- and long-term scenarios. Although the convergence of ADMM to the global solution cannot be generally guaranteed for MILP problems, we introduce two bounds on the optimal solution, allowing for the evaluation of the solution quality over iterations. Our numerical findings show that there is a trade-off between computational time and solution quality.

Keywords:Power systems, Delay systems, Stability of nonlinear systems Abstract: Consensus-based distributed secondary frequency control schemes have the potential to simultaneously ensure real time frequency restoration and economic dispatch in future power systems with large shares of renewable energy sources. Yet, due to their distributed nature these control schemes critically depend on communication between units and, thus, robustness with respect to communication uncertainties is crucial for their reliable operation. Furthermore, when applied in bulk power systems the control design and analysis should take higher-order turbine governor dynamics of the generation units explicitly into account. Both aspects have not been addressed jointly in the existing literature. Motivated by this, we derive conditions for robust stability of a consensus-based distributed frequency control scheme applied to a power system model with second-order turbine-governor dynamics in the presence of heterogeneous time-varying communication delays and dynamic communication topology. The result is established by a novel coordinate transformation and reduction to eliminate the invariant subspace in the closed-loop dynamics and by constructing a strict common Lyapunov-Krasovskii functional.

Keywords:Power systems, Lyapunov methods, Stability of nonlinear systems Abstract: The aggressive integration of distributed renewable sources is changing the dynamics of the electric power grid in an unexpected manner. As a result, maintaining conventional performance specifications, such as transient stability, may not be sufficient to ensure its reliable operation in stressed conditions. In this paper, we introduce a novel criteria in transient stability with consideration of operational constraints over frequency deviation and angular separation. In addition, we provide a robustness measure of the region of attraction, which can quantify the ability of the post-fault system to remain synchronized even under disturbances. To assess this new stability specification, we adopt the notion of Input-to-State Stability (ISS) to the context of power systems and introduce a new class of convex Lyapunov functions, which will result in tractable convex-optimization-based stability certificates. As a result, we are able to quantify the level of disturbance a power system can withstand while maintaining its safe operation. We illustrate the introduced stability specification and certificate on the IEEE 9 bus system.

Keywords:Power systems, Stability of nonlinear systems Abstract: Sufficient conditions for almost global synchronization of second-order multi-machine power systems with radial topology are provided. The analysis is based on the recently proposed multivariable cell structure approach using Leonov functions - an extension of the powerful cell structure principle developed by Leonov and Noldus to nonlinear systems, the dynamics of which are periodic with respect to several state variables and possess multiple invariant solutions. The efficiency of the derived conditions is illustrated via a numerical example.

Keywords:Power systems, Lyapunov methods, Uncertain systems Abstract: This paper analyzes the transient stability of power systems with uncertain parameters. More precisely, we suppose that the inertia constants and damping coefficients of generators are uncertain, and consider the problem of checking the stability of an equilibrium state for all possible values of the uncertain parameters, and estimating the intersection of the region of attraction for those parameter values. By using a polytope representation for the uncertain parameters, we present a method to solve the problem. In the presented method, we solve a sum of squares (SOS) programming problem based on the polytope representation. It is proven that if this SOS programming problem is feasible, then our method provides a solution to the analysis problem of the transient stability.

Keywords:Power generation, Robust adaptive control, Agents-based systems Abstract: This paper proposes a robust distributed secondary voltage restoration control protocol for inverter-based islanded microgrid. The problem is attacked from a cooperative-based control perspective an inspired to the tracking consensus paradigm. The task is achieved asymptotically by exploiting only delayed communications among distributed generators, while dispensing with the knowledge of local models, parameters, and in spite of the electrical coupling due to power lines and loads. Robustness is obtained thanks to the integration in the control protocol of an Integral Sliding Mode Control term. The actual control output is continuous and can be safely Pulse-Width Modulated by a fixed given frequency, as required to not hurt the switching power artifacts. A dedicated Lyapunov analysis providing a simple set of tuning rules is given. A Linear Matrix Inequality (LMI) criterion is also employed to estimate the maximum delay for communications. Finally, simulation results show the effectiveness of the proposed solution.

Keywords:Optimization, Communication networks, Randomized algorithms Abstract: This paper addresses a distributed optimization problem in a large communication network, where nodes are active sporadically. Each active node should properly control its action to maximize the global performance of the network, which is characterized by a pre-defined utility function. We consider a challenging situation where the optimization algorithm has to be performed only based on a scalar approximation of the utility function, rather than its closed-form expression, so that the typical gradient descent method cannot be applied. This setting is quite realistic when the network is affected by some stochastic and time-varying process, and that each node cannot have the full knowledge of the network states. We propose a distributed optimization algorithm and proves its almost surely convergence to the optimum. Numerical results are also presented to justify our claim.

Keywords:Optimization, Distributed control, Agents-based systems Abstract: We developed distributed continuous-time algorithms to solve the resource allocation problem with quadratic cost functions and continuously time-varying resources. Since the resources are time-varying, the optimal solution is changing over time. The allocation decision variable should not only find but also track the optimal solution trajectory. In a distributed manner, the agents work collaboratively to find as well as track the optimal solution using local information. Without the local allocation feasibility constraints, a distributed algorithm is designed based on sign function and consensus protocols. The tracking error is proven to vanish in finite time. When the local allocation feasibility constraints are considered, a distributed algorithm based on singular perturbation theory and penalty function is developed. The tracking error is proven to be uniformly ultimately bounded.

Keywords:Optimization, Optimization algorithms, Distributed control Abstract: In this work, a distributed multi-agent optimization problem is studied where different subsets of agents are coupled with each other through affine constraints. Moreover, each agent is only aware of its own contribution to the constraints and only knows which neighboring agents share constraints with it. An effective distributed first-order algorithm is developed, which requires sharing dual variables only and takes advantage of the constraint sparsity. The algorithm is shown to converge to the exact minimizer under sufficiently small constant step sizes. A simulation is given to illustrate the effect of the constraint structure and advantages of the proposed algorithm.

Keywords:Optimization, Learning, Simulation Abstract: Personalized recommendation systems (RS) are extensively used in many services. Many of these are based on learning algorithms where the RS uses the recommendation history and the user response to learn an optimal strategy. Further, these algorithms are based on the assumption that the user interests are rigid. Specifically, they do not account for the effect of learning strategy on the evolution of the user interests. In this paper we develop influence models for a learning algorithm that is used to optimally recommend websites to web users. We adapt the model of Ioannidis 2010 to include an item-dependent reward to the RS from the suggestions that are accepted by the user. For this we first develop a static optimization scheme when all the parameters are known. Next we develop a stochastic approximation based learning scheme for the RS to learn the optimal strategy when the user profiles are not known. Finally, we describe several user-influence models for the learning algorithm and analyze their effect on the steady user interests and on the steady state optimal strategy as compared to that when the users are not influenced.

Keywords:Optimization, Statistical learning, Optimization algorithms Abstract: This paper is concerned with the robust quadratic regression problem, where the goal is to find the unknown parameters (state) of a system modeled by nonconvex quadratic equations based on observational data. In this problem, a sparse subset of equations are subject to errors (noise values) of arbitrary magnitudes. We propose two techniques based on conic optimization to address this problem. The first one is a penalized conic relaxation, whereas the second one is a more complex iterative conic optimization equipped with a hard thresholding operator. We derive a deterministic bound for the penalized conic relaxation to quantify how many bad measurements the algorithm can tolerate without producing a nonzero estimation error. This bound is then analyzed for Gaussian systems, and it is proved that the proposed method allows up to a square root of the total number of measurements to be grossly erroneous. If the number of measurements is sufficiently large, we show that the iterative conic optimization method recovers the unknown state precisely even when up to a constant fraction of equations are arbitrarily wrong in the Gaussian case. The efficacy of the developed methods is demonstrated on synthetic data and a European power grid.

Keywords:Optimization, Optimization algorithms, Numerical algorithms Abstract: This paper analyses the performance of projected gradient descent on optimisation problems with cost functions and constraints that vary in discrete time. Specifically, strongly convex cost functions with Lipschitz gradient, and a sequence of convex constraints are assumed. Error bounds and sub-optimality bounds are derived for a variety of cases, which show convergence to a steady-state. Conditions on the constraint sequence are also presented for guaranteeing finite-time feasibility, and for bounding the distance between successive minimisers. Numerical examples are then presented to validate the analytical results.

Keywords:Optimal control, Hybrid systems Abstract: Cost evaluation problems for hybrid inclusions are studied. Sufficient conditions, in the form of Lyapunov-like inequalities, are provided to derive an upper bound on the cost associated with the solution to a hybrid inclusion with respect to a hybrid cost functional. Under additional sufficient conditions, we determine the cost exactly without computing solutions. Constructive results are proposed to solve cost evaluation problems in some relevant applications. Numerical examples are presented.

Keywords:Optimal control, Learning, Time-varying systems Abstract: This paper presents a data-driven method to obtain an approximate solution of the finite-horizon optimal control problem for linear time-varying discrete-time systems. Firstly, a finite-horizon Policy Iteration method for linear time-varying discrete-time systems is proposed. Then, a data-driven off-policy Policy Iteration algorithm is derived to find approximate optimal controllers when the system dynamics is unknown. Under mild conditions, the proposed data-driven off-policy algorithm converges to the optimal solution. Finally, the effectiveness of the derived method is validated by a numerical example.

Keywords:Optimal control, Control applications, Game theory Abstract: Detecting and preventing the data exfiltration of advanced persistent threats is a challenging problem. These attacks can remain in their target system for several years while retrieving information at a very slow rate, possibly after reformatting and encrypting the data they have accessed. Tainting and tracking some of the files in the system and deploying honeypots are two of the potentially effective measures against advanced persistent threats. In this paper, we introduce an analytical framework to study the effect of these measures on the amount of files that an attacker can exfiltrate. In particular, we obtain upper bounds on the expected amount of files at risk given a certain ratio of tainted and honey files in the system by using dynamic programming and Pontryagin's maximum principle. In addition, we show that in some cases tainting more of the files does not necessarily improve the security of the system. The results highlight the effectiveness and the necessity of deception for combatting advanced persistent threats.

Keywords:Optimal control, Lyapunov methods, Computational methods Abstract: This paper studies the feedback stabilization problem for deterministic nonlinear control systems described by ODEs. Assuming that a local control Lyapunov function (CLF) with certain properties can be explicitly constructed, we propose a way of extending it to a global CLF. Under a number of reasonable conditions, it is proved that the concatenation of the local CLF and the value function for an appropriately formulated exit-time optimal control problem leads to a global CLF satisfying the sought-after infinitesimal decrease property. The exit-time problem is stated with respect to a sublevel set of the local CLF. We then develop the theoretical foundations of a curse-of-dimensionality-free characteristics based approach for approximating the related value function. Future research directions and possible applications are also discussed.

Keywords:Optimal control, Constrained control, Communication networks Abstract: Motivated by various applications from Internet congestion control to power control in smart grids and electric vehicle charging, we study Generalized Additive Increase Multiplicative Decrease (G-AIMD) dynamics under impulsive control in continuous time with the time average alpha-fairness criterion. We first show that the control under relaxed constraints can be described by a threshold. Then, we propose a Whittle-type index heuristic for the hard constraint problem. We prove that in the homogeneous case the index policy is asymptotically optimal when the number of users is large.

Keywords:Optimal control, Linear systems, Biological systems Abstract: A common assumption in physiology about human motion is that the realized movements are done in an optimal way. The problem of recovering of the optimality principle leads to the inverse optimal control problem. Formally, in the inverse optimal control problem we should find a cost-function such that under the known dynamical constraint the observed trajectories are minimizing for such cost. In this paper we analyze the inverse problem in the case of finite horizon linear-quadratic problem. In particular, we treat the injectivity question, i.e. whether the cost corresponding to the given data is unique, and we propose a cost reconstruction algorithm. In our approach we define the canonical class on which the inverse problem is either injective or admit a special structure, which can be used in cost reconstruction.

Keywords:Agents-based systems, Cooperative control, Quantized systems Abstract: The goal of distributed average consensus in multi-agent systems is for the nodes, each associated with some initial value, to obtain the average (or some value close to the average) of these initial values. In this paper, we present and analyze a distributed averaging algorithm which operates exclusively on quantized values (specifically, the information stored, processed and exchanged between neighboring agents is subject to deterministic uniform quantization) and relies on event-driven updates (e.g., to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage). We characterize the properties of the proposed distributed averaging protocol and show that its execution, on any time-invariant and strongly connected digraph, will allow all agents to reach, in finite time, a common consensus value represented as the ratio of two integers that is equal to the exact average. We conclude with examples that illustrate the operation, performance, and potential advantages of the proposed algorithm.

Keywords:Agents-based systems, Hybrid systems, Networked control systems Abstract: In this paper we investigate a dynamic consensus problem for an {em open multi-agent system}. Open multi-agent systems are characterized by a time-varying set of agents connected by a network: agents may leave and new agents may join the network at any time, thus the term ``open". The dynamic consensus problem consists in achieving agreement about the time-varying average of a set of reference signals considered to be the agents' inputs. Dynamic consensus has recently found application in the context of distributed estimation for electric demand-side management, where a large population of connected domestic appliances needs to estimate its future average power consumption. Since the considered network of devices changes as new appliances log in and out, there is a need to develop and characterize dynamic consensus algorithms for these open scenarios. In this paper we give several initial contributions to a general theory of open multi-agent systems, as well as to the specific problem of dynamic consensus in this context. In a more theoretical perspective, we propose a formal definition of an open multi-agent systems, a suitable notion of stability, and some sufficient conditions to establish it. In a more concrete perspective, we design a dynamic consensus algorithm and characterize its convergence properties in an open-multi-agent systems: the Open Proportional Dynamic Consensus algorithm. Numerical simulations illustrate its evolution.

Keywords:Agents-based systems, Markov processes, Network analysis and control Abstract: We consider a multi-agent system in which agents arrive and depart from a network randomly as a Bernoulli process. Each agent that is active in the network must decide between two actions represented by 0 or 1. Each active agent then observes the action of a random neighbour and updates its preference towards a certain action. New agents that arrive into the network are activated with a random preference and action. This means that the notion of consensus in the standard sense can no longer be applied and instead, we provide conditions under which majority action preservation occurs when the number of agents is arbitrarily large. This property will imply that a large fraction of the active agent population will retain their action almost surely.

Keywords:Agents-based systems, Cooperative control, Autonomous systems Abstract: In this paper, a new perfect matching algorithm for two sets of agents of the same sizes is proposed by simply following the electrostatic fields (ESF) in higher dimensional space. The algorithm also generates trajectories for each agent to avoid collisions between the same types. The proposed ESF follows the gradient descent of the harmonic potential function. It is shown that there are no saddle points, but there exists an invariant manifold which may evolve all agents to some consensus point. However, this invariant manifold (IM) is measure zero in the state space, and a sufficient condition for IM being unstable is proposed. Inspired by electrostatic forces with nonuniform charges, a weighted electrostatic field is proposed by following the gradient descent of a subharmonic function. Similarly, safe trajectories are generated with perfect matching, but the final assignment may be different from the original ESF method. A simulation result for the performance of the matching (an average L_2 distance among the matching) is shown at the end and compared with the optimal (Hungarian) method.

Keywords:Agents-based systems, Distributed control, Autonomous systems Abstract: We study the general formation problem for a group of mobile agents in a plane, in which the agents are required to maintain a distribution pattern, as well as to rotate around or remain static relative to a static/moving target. The prescribed distribution pattern is a class of general formations that the distances between neighboring agents or the distances from each agent to the target do not need to be equal. Each agent is modeled as a double integrator and can merely perceive the relative information of the target and its neighbors. A distributed control law is designed using the limit-cycle based idea to solve the problem. One merit of the controller is that it can be implemented by each agent in its Frenet-Serret frame so that only local information is utilized without knowing global information. Theoretical analysis is provided of the equilibrium of the N-agent system and of the convergence of its converging part. Numerical simulations are given to show the effectiveness and performance of the proposed controller.

Keywords:Sampled-data control, Learning, Optimal control Abstract: This paper presents a novel Q-learning based dynamic intermittent mechanism to control linear systems evolving in continuous time. In contrast to existing event-triggered mechanisms, where complete knowledge of the system dynamics is required, the proposed dynamic intermittent control obviates this requirement while providing a quantified level of performance. An internal dynamical system will be introduced to generate the triggering condition. Then, a dynamic intermittent Q-learning is developed to learn the optimal value function and the hybrid controller. A qualitative performance analysis of the dynamic event-triggered control is given in comparison to the continuous-triggered control law to show the degree of sub-optimality. The combined closed-loop system is written as an impulsive system, and it is proved to have an asymptotically stable equilibrium point without any Zeno behavior. A numerical simulation of an unknown unstable system is presented to show the efficacy of the proposed approach.

Keywords:PID control, Sampled-data control, Delay systems Abstract: We study a sampled-data implementation of the PID controller. Since the derivative is hard to measure directly, it is approximated using a finite difference giving rise to a delayed sampled-data controller. We suggest a novel method for the analysis of the resulting closed-loop system that allows to use only the last two measurements, while the existing results used a history of measurements. This method also leads to essentially larger sampling period. We show that, if the sampling period is small enough, then the performance of the closed-loop system under the sampled-data PID controller is preserved close to the one under the continuous-time PID controller. The maximum sampling period is obtained from LMIs derived using an appropriate Lyapunov-Krasovskii functional. These LMIs allow to consider systems with uncertain parameters. Finally, we develop an event-triggering mechanism that allows to reduce the amount of sampled control signals used for stabilization.

Keywords:Networked control systems, Quantized systems, Uncertain systems Abstract: This letter studies unstable scalar continuous-time systems with uncertain parameters that are controlled over a network with finite capacity with possible uncertain, but uniformly bounded, time-varying transmission delays. While the decoder and controller are assumed to be static and memoryless, we are particularly interested in the role of the sampling mechanism that is allowed to be event-based, i.e., dependent on the state. The control goal is to guarantee containability and to characterize the minimal requirements in terms of asymptotic average bit and triggering rates for satisfying this objective. Our first investigation neglects the transmission delay and focuses on the importance of the alphabet due to uncertain system parameters. The remainder of the study characterizes the general case, by deriving general bounds on the allowable delay and the asymptotic average bit and triggering rates for two alphabets. The letter closes with a comparison of the derived bounds and conclusions that can be drawn regarding the choice of the alphabet.

Keywords:Networked control systems, Machine learning, Neural networks Abstract: Event-triggered control (ETC) methods can achieve high-performance control with a significantly lower number of samples compared to usual, time-triggered methods. These frameworks are often based on a mathematical model of the system and specific designs of controller and event trigger. In this paper, we show how deep reinforcement learning (DRL) algorithms can be leveraged to simultaneously learn control and communication behavior from scratch, and present a DRL approach that is particularly suitable for ETC. To our knowledge, this is the first work to apply DRL to ETC. We validate the approach on multiple control tasks and compare it to model-based event-triggering frameworks. In particular, we demonstrate that it can, other than many model-based ETC designs, be straightforwardly applied to nonlinear systems.

Keywords:Discrete event systems, Stability of nonlinear systems, Control of networks Abstract: This paper revisits the problem of designing opportunistic state-triggered conditions for stabilization, focusing on the balance between conserving resources (e.g., minimizing the number of triggers) and meeting a desired level of performance. Traditionally, event-triggered control design focuses on ensuring stabilization while conservatively enforcing that the specified performance is met. We take a different approach by considering the desired performance as part of the trigger design. Inspired by the concept of Control Barrier Function, our proposed design allows the system to deviate from Lyapunov’s condition for asymptotic stability when the system is doing well in term of performance. We characterize the benefits of the proposed approach in terms of increased inter-event time, robustness to delays in the evaluation of the trigger, and flexibility for distributed implementation.

Keywords:Networked control systems, Nonlinear output feedback, Robust control Abstract: We investigate the stabilization of perturbed nonlinear systems using output-based periodic event-triggered controllers. Thus, the communication between the plant and the controller is triggered by a mechanism, which evaluates an output- and input-dependent rule at given sampling instants. We address the problem by emulation. Hence, we assume the knowledge of a continuous-time output feedback controller, which robustly stabilizes the system in the absence of network. We then implement the controller over the network and model the overall system as a hybrid system. We design the event-triggered mechanism to ensure an input-to-state stability property. An explicit bound on the maximum allowable sampling period at which the triggering rule is evaluated is provided. The analysis relies on the construction of a novel hybrid Lyapunov function. The results are applied to a class of Lipschitz nonlinear systems, for which we formulate the required conditions as a linear matrix inequality. The effectiveness of the scheme is illustrated via simulations of a nonlinear example.

Keywords:Optimization algorithms, Communication networks, Agents-based systems Abstract: In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method. We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant step size choice). More importantly, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size, which is a comparable performance to a centralized stochastic gradient algorithm. Numerical examples further demonstrate the effectiveness of the method.

Keywords:Optimization, Distributed control, Large-scale systems Abstract: In this paper, we consider the distributed optimization problem, whose objective is to minimize the global objective function, which is the sum of local convex objective functions, by using local information exchange. To avoid continuous communication among the agents, we propose a distributed algorithm with a dynamic event-triggered communication mechanism. We show that the distributed algorithm with the dynamic event-triggered communication scheme converges to the global minimizer exponentially, if the underlying communication graph is undirected and connected. Moreover, we show that the event-triggered algorithm is free of Zeno behavior. For a particular case, we also explicitly characterize the lower bound for inter-event times. The theoretical results are illustrated by numerical simulations.

Keywords:Optimization algorithms, Network analysis and control, Numerical algorithms Abstract: This paper proposes a distributed optimization framework for solving nonlinear programming problems with separable objective function and local constraints. Our novel approach is based on first reformulating the original problem as an unconstrained optimization problem using continuously differentiable exact penalty function methods and then using gradient based optimization algorithms. The reformulation is based on replacing the Lagrange multipliers in the augmented Lagrangian of the original problem with Lagrange multiplier functions. The problem of calculating the gradient of the penalty function is challenging as it is non-distributed in general even if the original problem is distributed. We show that we can reformulate this problem as a distributed, unconstrained convex optimization problem. The proposed framework opens new opportunities for the application of various distributed algorithms designed for unconstrained optimization.

Keywords:Optimization algorithms, Control of networks, Distributed control Abstract: In this letter, we study distributed optimization, where a network of agents, abstracted as a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing approaches over directed graphs are based on push-sum (type) techniques, which use an independent algorithm to asymptotically learn either the left or right eigenvector of the underlying weight matrices. This strategy causes additional computation, communication, and nonlinearity in the algorithm. In contrast, we propose a textit{linear} algorithm based on an inexact gradient method and a gradient estimation technique. Under the assumptions that each local function is strongly-convex with Lipschitz-continuous gradients, we show that the proposed algorithm geometrically converges to the global minimizer with a sufficiently small step-size. We present simulations to illustrate the theoretical findings.

Keywords:Agents-based systems, Cooperative control, Optimization algorithms Abstract: This paper studies a spatiotemporal connectivity-preserving rendezvous problem for a group of mobile robots. With the available battery and communication cost being taken into account, this problem is split into two sub-problems. Firstly, robots need to choose optimal strategies by solving a distributed constrained optimization problem to determine when and where to meet before moving. Consensus-based distributed gradient algorithms are developed to solve this subproblem. Subsequently, once the optimal solution is obtained and provided to only a subset of robots, a fixed-time distributed controller is designed to solve a connectivity-preserving rendezvous control problem. It is shown that the robot team under the proposed designs can achieve the spatiotemporal connectivity-preserving rendezvous task, while minimizing the energy consumption.

Keywords:Optimization algorithms, Distributed control, Agents-based systems Abstract: In this paper we study a distributed optimization problem for continuous time multi-agent systems. In our setting, the global objective for the multi-agent system is to minimize the sum of locally coupled strictly convex cost functions. Notably, this class of optimization objectives can be used to encode several important problems such as distributed estimation. For this problem setting, we propose a distributed signed gradient descent algorithm, which relies on local observers to retrieve 2-hop state information that are required to compute the descent direction. Adaptive gains for the local observer are introduced to render the convergence independent from: i) the structure of the network topology and ii) the local gains of the per-agent signed gradient-descent update law. The finite-time convergence of the local observer and of the proposed signed gradient descent method is demonstrated. Numerical simulations involving a distributed weighted least-square (WLS) estimation problem, with the aim of identifying in the context of an advanced water management system for precision-farming the soil thermal properties in a large-scale hazelnut orchard, have been proposed to corroborate the theoretical findings.

Keywords:Traffic control, Stochastic systems Abstract: In this paper, we propose a control-oriented model for mobility-on-demand systems (MOD). The system is first described through dynamical stochastic state-space equations in discrete time, and then suitably simplified in order to obtain a control-oriented model, on which a control strategy based on Model Predictive Control (MPC) is devised. The control strategy aims at maintaining the average number of vehicles at stations within prescribed bounds. Relevant features of the proposed model are: i) the possibility of considering stochasticity and heterogeneity in the system parameters; ii) a state space structure, which makes the model suitable for implementation of effective parameter identification and control strategies; and iii) the possibility of weighting the control effort, leading to control solutions that may trade off efficiency and cost. Simulation results on a synthetic network corroborate the validity of our approach under several operational conditions.

Keywords:Traffic control, Transportation networks, Mean field games Abstract: We study a route choice game model, where a large number of drivers are circulating on a road network. Given an origin-destination pair, each driver tries to pick the shortest least congested route to minimize his/her travel time. We develop a mean field game based algorithm that generates the drivers’ optimal choices and anticipates the evolution of their probability distribution on the network. The optimal choices, which constitute a Nash equilibrium in the limit of an infinite number of drivers, guide a generic driver to his/her destination with the most efficient road. Moreover, they define a maximum likelihood function that can be used to estimate the model’s parameters. Our algorithm takes only the drivers’ initial distribution as an input, which is typically provided to the drivers by navigation applications. Finally, we illustrate via a numerical scheme how the model can also be used to evaluate the performance of different network configurations. An example shows how adding a road link to an existing network cannot improve the expected travel time of the drivers.

Keywords:Traffic control, Automotive control, Autonomous robots Abstract: We propose a hybrid decision-making framework for safe and efficient autonomous driving of selfish vehicles on highways. Specifically, we model the dynamics of each vehicle as a Mixed-Logical-Dynamical system and propose simple driving rules to prevent potential sources of conflict among neighboring vehicles. We formalize the coordination problem as a generalized mixed-integer potential game, where an equilibrium solution generates a sequence of mixed-integer decisions for the vehicles that trade off individual optimality and overall safety.

Keywords:Traffic control, Transportation networks, Optimization algorithms Abstract: This paper proposes a simplified version of classical models for urban transportation networks, and studies the problem of controlling intersections with the goal of optimizing network-wide congestion. Differently from traditional approaches to control traffic signaling, our simplified framework allows a more tractable analysis of the network dynamics and, yet, accurately captures the behavior of traffic flows along roads and in proximity of intersections in regimes of free flow. We cast an optimization problem to describe the goal of optimally controlling automated intersections, and relate congestion objectives with the problem of optimizing a metric of controllability of the associated dynamical system. We characterize the system performance in relation to (sub)optimal configurations, and identify conditions that guarantee network stability. Lastly, we assess the benefits of the proposed modeling and optimization framework through a microscopic simulator.

Keywords:Traffic control, Transportation networks Abstract: This work considers the assignment of vehicle traffic consisting of both individual, opportunistic vehicles and a cooperative fleet of vehicles. The first set of vehicles seek a user-optimal policy and the second set seeks a fleet-optimal policy. We provide explicit sufficient conditions for the existence and uniqueness of a Nash equilibrium at which both policies are satisfied.

We also propose two different algorithms to determine the equilibrium, one centralized and one decentralized. Furthermore, we present a control scheme to attain such an equilibrium in a dynamical network flow. An example is considered showing the workings of our scheme and numerical results are presented.

Keywords:Petri nets, Discrete event systems, Air traffic management Abstract: In this paper, we deal with the problem of critical observability for discrete event systems modeled by labeled safe Petri nets (PNs). Critical observability is a property originated from the safety-critical applications of cyber-physical systems. For the purpose to check this property of a PN model, it is necessary to detect whether the current state of the net system is, or is not in a set of critical states representing dangerous operations. The main results of the work is to propose a necessary and sufficient condition for checking the critical observability in safe PNs when the set of critical states is modeled by an arbitrary set of reachable markings. The proposed method exploits the solution of integer linear programming problems. Finally, several examples are discussed to demonstrate the efficiency of the proposed approach.

Keywords:Stochastic systems Abstract: In the deterministic systems case, D-scaling is known to be effective for reducing conservativeness in stability analysis of closed-loop systems consisting of two subsystems. This paper considers discrete-time stochastic systems and proposes a new approach called stochastic D-scaling. In this approach, we deal with not only a deterministic scaling element but also a stochastic scaling element having the nature relevant to the randomness behind stochastic systems. The scaling elements are assumed to be given in this paper. Then, the effectiveness of the stochastic D-scaling is demonstrated through numerical examples.

Keywords:Stochastic systems, Markov processes, Optimization Abstract: Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary distribution and average variance, it seeks the diffusion process with optimal convergence rate. It is shown that the optimal drift function is a linear function and the convergence rate of the stochastic process is bounded by the ratio of the average variance to the variance of the stationary distribution. Furthermore, the concavity of the optimal relaxation time as a function of the stationary distribution has been proven, and it is shown that all Pearson diffusion processes of the Hypergeometric type with polynomial functions of at most degree two as the variance functions are optimal.

Keywords:Automata, Stochastic systems, Markov processes Abstract: We derive an algorithm to compute satisfiability bounds for arbitrary omega-regular properties in an Interval-valued Markov Chain (IMC) interpreted in the adversarial sense. IMCs generalize regular Markov Chains by assigning a range of possible values to the transition probabilities between states. In particular, we expand the automata-based theory of omega-regular property verification in Markov Chains to apply it to IMCs. Any omega-regular property can be represented by a Deterministic Rabin Automata (DRA) with acceptance conditions expressed by Rabin pairs. Previous works on Markov Chains have shown that computing the probability of satisfying a given omega-regular property reduces to a reachability problem in the product between the Markov Chain and the corresponding DRA. We similarly define the notion of a product between an IMC and a DRA. Then, we show that in a product IMC, there exists a particular assignment of the transition values that generates a largest set of non-accepting states. Subsequently, we prove that a lower bound is found by solving a reachability problem in that refined version of the original product IMC. We derive a similar approach for computing a satisfiability upper bound in a product IMC with one Rabin pair. For product IMCs with more than one Rabin pair, we establish that computing a satisfiability upper bound is equivalent to lower-bounding the satisfiability of the complement of the original property. A search algorithm for finding the largest accepting and non-accepting sets of states in a product IMC is proposed. Finally, we demonstrate our findings in a case study.

Keywords:Learning, Stochastic optimal control, Decentralized control Abstract: We consider a two-agent team learning problem over an infinite time horizon under two different dynamics and information sharing models: i) Decoupled dynamics with no information sharing, ii) Coupled dynamics with one-step delayed information sharing. The state transition kernels are parametrized by an unknown but fixed parameter taking values in a finite space. We study a decentralized Thompson sampling based approach to learn the underlying parameter where each agent maintains a belief about the underlying parameter. The agents draw a sample from their beliefs at each time and select their action using the benchmark policy for the sampled parameter. We show that under some assumptions on the state transition kernels, the regret achieved by Thompson sampling is upper bounded by a constant independent of the time horizon.

Keywords:Stochastic systems, Linear parameter-varying systems, Game theory Abstract: Robust incentive Stackelberg games for stochastic linear parameter-varying (LPV) systems with multiple decision makers are investigated. After the establishment of the modified stochastic bounded real lemma, the linear quadratic control (LQC) for stochastic LPV systems with time-independent fixed gain is formulated. A robust incentive Stackelberg strategy is introduced to induce the follower's actions such that the follower's Pareto optimal solutions are obtained under H_infty constraint. The solvability conditions of the problem are established by using cross-coupled matrix inequalities (CCMIs). It is shown that the proposed strategy set can be computed recursively using a numerical algorithm based on linear matrix inequalities (LMIs). The efficiency of the proposed algorithm is demonstrated using a numerical example.

Keywords:Stochastic systems, Computational methods Abstract: Stochastic linearization is a useful method to analyse a class of nonlinear stochastic dynamical systems. An important feature is that it requires no Monte Carlo simulation, which is advantageous especially for dynamics whose extremal outliers are not negligible. However, the resulting accuracy has so far been examined only by numerical experiments, which is usually comparison with Monte Carlo simulation. In view of this, we derive novel error bounds for stochastic linearization of feedback systems in this paper. The practical usefulness is examined through a numerical example.

Keywords:Lyapunov methods, Genetic regulatory systems, Stability of nonlinear systems Abstract: A piecewise affine (PWA) model of a gene regulatory network is considered. After an introduction to the model, the problem of finding a generally non-smooth function V(x) which is non increasing along the system trajectories is addressed and a way of solving it is given in terms of an LMI's feasibility problem. The presence of sliding modes in the system is explicitly considered and conditions of non-increase of V(x) along these are stated in terms of LMIs. Finally, we present an example which show the resulting V(x) obtained by solving the feasibility problem described.

Here, we focus on a proposed design framework, which is able to approximate the input-output behaviour of key linear operators used in feedback control circuits by combining three elementary chemical reactions.

The implementation of such circuits using DNA strand displacement introduces non-linear internal dynamics due to annihilation reactions among different molecular species. In addition, experimental implementation of in-silico designs introduces significant levels of uncertainty and variability in reaction rate constants and equilibrium concentrations.

Previous work using this framework has overlooked the practical implications of these issues for the construction of nucleic acid-based feedback control circuits. Here, we analyse the impact of these nonlinearities and uncertainties on the stability of a biomolecular feedback loop. We show that a rigorous analysis of its nucleic acid- based implementation requires an investigation of the associated non-linear dynamics, to decide on realisable parameters and acceptable equilibrium concentrations.

We also show how the level of experimental uncertainty that is tolerated by the feedback circuit can be quantified using the structured singular value. Our results constitute a first step towards the development of a rigorous robustness analysis framework for nucleic acid-based feedback control circuits.

Keywords:Biomolecular systems, Systems biology, Biological systems Abstract: Nonlinear relaxation oscillators in engineering rely on positive feedback to operate. One category of relaxation oscillators is given by astable multivibrators, that include a bistable component at the core of their architecture. Here we describe a molecular network motif that operates as an astable multivibrator, and relies on a bistable switch (the classical Gardner and Collins genetic switch) that is toggled between its stable steady states by a persistent input. We show that oscillations arise in the presence of two negative feedback loops that process the persistent input and influence the production of the molecular species forming the bistable subsystem. We perform a thorough stability analysis of this motif obtaining closed-form practical conditions for the emergence of oscillations, and we examine the sensitivity of the system to parameter variations.

Keywords:Biological systems, Optimization algorithms, Nonlinear systems identification Abstract: High-throughput data acquisition in synthetic biology leads to an abundance of data that need to be processed and aggregated into useful biological models. Building dynamical models based on this wealth of data is of paramount importance to understand and optimize designs of synthetic biology constructs. However, building models manually for each data set is inconvenient and might become infeasible for highly complex synthetic systems. In this paper, we present state-of-the-art system identification techniques and combine them with chemical reaction network theory (CRNT) to generate dynamic models automatically. On the system identification side, Sparse Bayesian Learning offers methods to learn from data the sparsest set of base functions necessary to capture the dynamics of the system into ODE models; on the CRNT side, building on such sparse ODE models, all possible network structures within a given parameter uncertainty region can be computed. Additionally, the system identification process can be complemented with constraints on the parameters to, for example, enforce stability or non-negativity---thus offering relevant physical constraints over the possible network structures. In this way, the wealth of data can be translated into biologically relevant network structures, which then steers the data acquisition, thereby providing a vital step for closed-loop system identification.

Keywords:Biomolecular systems, Systems biology, Cellular dynamics Abstract: Biological control systems often contain a wide variety of feedforward and feedback mechanisms that regulate a given process. While it is generally assumed that this apparent redundancy has evolved for a reason, it is often unclear how exactly the cell benefits from more complex circuit architectures. Here we study this problem in the context of a minimal model of the Heat Shock Response system in E. coli and show, through a combination of theory and simulation, that the complexity of the natural system outperforms hypothetical simpler architectures in a variety of robustness and efficiency trade-offs. We have developed a significantly simplified model of the system that faithfully captures these rich issues. Because a great deal of biological detail is known about this particular system, we are able to compare simple models with more complete ones and obtain a level of theoretical and quantitative insight not generally feasible in the study of biological circuits. We primarily hope this will inform future analysis of both heat shock and newly studied biological complexity.

Keywords:Genetic regulatory systems, Biotechnology Abstract: Competition for gene expression resources within cellular systems limits the modularity of synthetic circuits, and can lead to the emergence of hidden regulatory interactions between different circuit genes. Experimental evidence suggests that the finite number of free ribosomes in the cell limits protein synthesis capacity and can create unforeseen coupling between co-expressed circuit genes that can result in performance degradation or even circuit failure. Recent work has shown that the cell's ribosome population can be subdivided into host-specific and circuit-specific functions by the production of quasi-orthogonal ribosomes. In this paper, we investigate the design of an integral feedback controller which acts to dynamically allocate ribosomes between host and circuit genes in order to reduce circuit-circuit coupling. We show that whilst the controller is able to successfully allocate resources and improve circuit performance, a non-zero steady state error remains. We show that interactions between the host cell's physiology and the synthetic circuitry act to prevents perfect integral action for the proposed controller architecture.

Keywords:Game theory, Markov processes, Stochastic systems Abstract: We analyze in this paper how a deceptive information provider can shape the shared information in order to control a decision maker's decisions. Data-driven engineering applications, e.g., machine learning and artificial intelligence, build on information. However, this implies that information (and correspondingly information providers) can have influential impact on the decisions made. Notably, the information providers can be deceptive such that they can benefit, while the decision makers suffer, from the strategically shaped information. We formulate (and provide an algorithm to compute) the optimal deceptive shaping policies in the multi-stage disclosure of, {em general}, multi-dimensional Gauss-Markov information. To be able to deceive the decision maker, the information provider should anticipate the decision maker's reaction while facing a trade-off between deceiving at the current stage and the ability to deceive in the future stages. We show that optimal shaping policies are linear within the general class of Borel-measurable policies even though the information provider and the decision maker could be seeking to minimize quite different quadratic cost functions.

Keywords:Game theory, Energy systems, Smart grid Abstract: Under the incentive-compatible Vickrey-Clarke-Groves mechanism, coalitions of participants can influence the auction to obtain higher collective profit. These manipulations were proven to be eliminated if and only if the market objective is supermodular. Nevertheless, several auctions do not satisfy the stringent conditions for supermodularity. These auctions include electricity markets, which are the main motivation of our paper. To address this issue, we introduce the supermodularity ratio and the weak supermodularity. We show that these concepts provide us with tight bounds on the profitability of collusion and shill bidding. We then derive an analytical lower bound on the supermodularity ratio. Our results are verified with case studies based on the IEEE test systems.

Keywords:Game theory, Markov processes, Differential-algebraic systems Abstract: As a subclass of stochastic differential games with algebraic constraints, this article studies dynamic noncooperative games where the constraints are described by jump Markov differential-algebraic equations (DAEs). Theoretical tools, which require computing the infinitesimal generator and deriving Hamiton-Jacobi-Bellman equation for Markov jump DAEs, are developed. These fundamental results lead to pure feedback optimal strategies to compute the Nash equilibrium in noncooperative setting. In case of quadratic cost and linear dynamics, these strategies are obtained by solving coupled Riccati differential equations. The problem of robust control can be formulated as a two-player zero sum game and is solved by applying the results developed in this paper.

Keywords:Networked control systems, Game theory, Decentralized control Abstract: Many decentralized and networked control problems involve decision makers which have either misaligned criteria or subjective priors. In the context of such a setup, in this paper we consider binary signaling problems in which the decision makers (the transmitter and the receiver) have subjective priors and/or misaligned objective functions. Depending on the commitment nature of the transmitter to his policies, we formulate the binary signaling problem as a Bayesian game under either Nash or Stackelberg equilibrium concepts and establish equilibrium solutions and their properties. In addition, the effects of subjective priors and costs on Nash and Stackelberg equilibria are analyzed. It is shown that there can be informative or non-informative equilibria in the binary signaling game under the Stackelberg assumption, but there always exists an equilibrium. However, apart from the informative and non-informative equilibria cases, under certain conditions, there does not exist a Nash equilibrium when the receiver is restricted to use deterministic policies. For the corresponding team setup, however, an equilibrium typically always exists and is always informative. Furthermore, we investigate the effects of small perturbations in priors and costs on equilibrium values around the team setup (with identical costs and priors), and show that the Stackelberg equilibrium behavior is not robust to small perturbations whereas the Nash equilibrium is.

Keywords:Game theory, Stochastic systems Abstract: Dynamic Information Flow Tracking (DIFT) has been proposed to detect stealthy and persistent cyber attacks that evade existing defenses such as firewalls and signature-based antivirus systems. A DIFT defense taints and tracks suspicious information flows across the network in order to identify possible attacks, at the cost of additional memory overhead for tracking non-adversarial information flows. In this paper, we present the first analytical model that describes the interaction between DIFT and adversarial information flows, including the probability that the adversary evades detection and the performance overhead of the defense. Our analytical model consists of a multi-stage game, in which each stage represents a system process through which the information flow passes. We characterize the optimal strategies for both the defense and adversary, and derive efficient algorithms for computing the strategies. Our results are evaluated on a real world attack dataset obtained using the Refinable Attack Investigation (RAIN) framework, enabling us to draw conclusions on the optimal adversary and defense strategies, as well as the effect of valid information flows on the interaction between adversary and defense.

Keywords:Game theory, Optimization, Large-scale systems Abstract: Several works have recently suggested to model the problem of coordinating the charging needs of a fleet of electric vehicles as a game, and have proposed distributed algorithms to coordinate the vehicles towards a Nash equilibrium of such game. However, Nash equilibria have been shown to posses desirable system-level properties only in simplified cases. In this work, we use the concept of price of anarchy to analyze the inefficiency of Nash equilibria when compared to the social optimum solution. More precisely, we show that i) for linear price functions depending on all the charging instants, the price of anarchy converges to one as the population of vehicles grows; ii) for price functions that depend only on the instantaneous demand, the price of anarchy converges to one if the price function takes the form of a positive pure monomial; iii) for general classes of price functions, the asymptotic price of anarchy can be bounded. For finite populations, we additionally provide a bound on the price of anarchy as a function of the number vehicles in the system. We support the theoretical findings by means of numerical simulations.

Keywords:Statistical learning, Learning, Machine learning Abstract: In preference learning, it is beneficial to incorporate monotonicity constraints for learning utility functions when there is prior knowledge of monotonicity. We present a novel method for learning utility functions with monotonicity constraints using Gaussian process regression. Data is provided in the form of pairwise comparisons between items. Using conditions on monotonicity for the predictive function, an algorithm is proposed which uses the weighted average between prior linear and maximum a posteriori (MAP) utility estimates. This algorithm is formally shown to guarantee monotonicity of the learned utility function in the dimensions desired. The algorithm is tested in a Monte Carlo simulation case study, in which the results suggest that the learned utility by the proposed algorithm performs better in prediction than the standalone linear estimate, and enforces monotonicity unlike the MAP estimate.

Keywords:Human-in-the-loop control, Statistical learning, Markov processes Abstract: Recent years have seen human-robot collaboration (HRC) quickly emerged as a hot research area at the intersection of control, robotics, and psychology. While most of the existing work in HRC focused on either low-level human-aware motion planning or HRC interface design, we are particularly interested in a formal design of HRC with respect to high-level complex missions, where it is of critical importance to obtain an accurate and tractable human model. Instead of assuming the human model is given, we ask whether it is reasonable to learn human models from observed data, such as the gesture, eye movements, head motions. We adopt a partially observable Markov decision process (POMDP) model in this work, as mounting evidence has suggested Markovian properties of human behaviors from psychology studies. In addition, POMDP provides a general modeling framework for sequential decision making where states are hidden and actions have stochastic outcomes. Distinct from the majority of POMDP model learning literature, we do not assume that the state, the transition structure or the bound of the number of states are given. Instead, we use a Bayesian non-parametric learning approach to decide the potential human states from data. Then we adopt an approach inspired by probably approximately correct (PAC) learning to obtain not only an estimation of the transition probability but also a confidence interval associated with the estimation. The performance of applying the control policy derived from the estimated model is guaranteed to be sufficiently close to the true model. Finally, data collected from a driver-assistance test-bed are used to illustrate the effectiveness of the proposed learning method.

Keywords:Statistical learning, Machine learning, Stochastic systems Abstract: Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide guarantees for application scenarios. Gaussian process regression represents one approach which provides such an indicator for the model confidence. However, this measure is only valid if the covariance function and its hyperparameters fit the underlying data generating process. In this paper, we derive an upper bound for the mean square prediction error of misspecified Gaussian process models based on a pseudo-concave optimization problem. We present application scenarios and a simulation to compare the derived upper bound with the true mean square error.

School of Engineering and Applied Sciences, HarvardUniversity

Keywords:Statistical learning, Machine learning Abstract: The randomized-feature technique has been successfully applied to large-scale supervised learning. Despite being significantly more efficient compared to kernel methods in terms of computational cost, random features can be improved from generalization (prediction accuracy) viewpoint. Recently, it has been shown that such improvement can be achieved using data-dependent randomization. We recently proposed an algorithm based on a data-dependent score function that explores the set of possible random features and exploits the promising regions. The method has shown promising empirical success (on various datasets) in terms of generalization error compared to the state-of-the-art in random features. Restricting our attention to cosine feature maps, in this work, we provide exact theoretical constraints under which the score function converges to the spectrum of the best model in the learning class. We further present another application of the method in Epileptic Seizure Recognition.

Keywords:Adaptive control, Control applications, Machine learning Abstract: We extend a recently proposed data-driven control technique for reference tracking to a class of Multi-Input Multi-Output (MIMO) systems where the coupling between the different states is "weak" in the sense of an induced norm. Using analysis results from the earlier work and by augmenting it with small-gain arguments for the coupling terms, we extend the analysis to MIMO systems. Additionally, a systematic procedure is proposed to tune and estimate the controller parameters. The data-driven controller is implemented in simulation and on an experimental Control Moment Gyroscope (CMG) test bed. The effectiveness of the technique is demonstrated by comparing the tracking performance to an LPV controller.

Keywords:Machine learning, Network analysis and control, Large-scale systems Abstract: We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed emph{coarse scalar curvature}, generalizes a recent definition of Ricci curvature for Markov chains on metric spaces by Ollivier [Journal of Functional Analysis 256 (2009) 810-864], and is related to the scalar curvature when the hypergraph arises naturally from a Riemannian manifold. We investigate basic properties of the coarse scalar curvature and obtain several bounds. Empirical experiments indicate that coarse scalar curvatures are capable of detecting ``bridges'' across connected components in hypergraphs, suggesting it is an appropriate generalization of curvature on simple graphs.

Keywords:Robotics, Optimization, Algebraic/geometric methods Abstract: This paper proposes a joint optimization scheme of the structural design and control of a fully-actuated hexrotor unmanned aerial vehicle. The hexrotor dynamics is formulated on the special Euclidean group SE(3) which represents the position and attitude of a rigid body. An optimal control problem on SE(3) is then considered, and the optimal input and the associated viscosity solution of the Hamilton-Jacobi-Bellman equation are presented analytically. The solution, value function, expresses the minimum value of the cost function for a given initial state. The analytical form of the value function is then regarded as a function of structural variables, and the function is minimized by modifying the vehicle structure. A numerical example shows that the optimally-controlled optimal structure maximizes its dynamic manipulability measure. Moreover, the resulting structure and control system are shown to be energy-efficient.

Keywords:Robotics, Control applications, Variable-structure/sliding-mode control Abstract: A new control law for joint-space impedance in robots with variable impedance actuators is presented. The objective is achieved using reduced information on high order derivatives compared to standard approaches, therefore leading to more reliable interactions with unknown environments. Most importantly, the impedance characteristic is given by the real stiffness and damping coefficients of each actuator, therefore updating strategies of the latter directly modify the system response obtained on the link side. The method is evaluated both in simulations and experiments. Additionally, the control law is also adapted for systems with series elastic actuators.

Keywords:Robotics, Markov processes, Stochastic optimal control Abstract: This paper presents a Markov decision process based model for a socially assistive robot. Problem addressed by the model is one to one correspondence of a robot with a human where robot has to convince the human about completing certain tasks. In this regard, emotions of the human and those of the robot are incorporated in the model. Furthermore, emotion transition probabilities and probabilities of robot being able to successfully convince the human are also incorporated. The resulting model however involves large state space. Computational complexity involved in calculation of optimal decision policy from the proposed model is discussed. Consequently, a computational complexity reduction technique is proposed that uses decomposition of the tasks to be performed into sub groups. An online learning framework is also proposed to account for un-modeled parameters in the problem. Behavior of decision making optimal policy obtained from the proposed model has been demonstrated with the help of a simulation based case study.

Keywords:Robotics, Nonholonomic systems, Large-scale systems Abstract: A multilink inverted pendulum connected to a cart moving in a same vertical plane is typical underactuated mechanical system studied in both control and robotic communities. This paper presents the motion equation for an n-link inverted pendulum in a cart without any assumption on the physical parameters of the pendulum. Based on the motion equation and some properties of the physical parameters of the pendulum, this paper proves that such a system is linearly controllable around its upright equilibrium point (all its links in the upright position and the cart in the origin) for all its possible physical parameters; that is, such a system is linearly strongly structurally controllable around the point. This paper validates the above result via two existing physical systems of 3-link inverted pendulum in a cart.

Keywords:Robotics, Stochastic systems, Observers for nonlinear systems Abstract: This work proposes a nonlinear stochastic filter evolved on the Special Orthogonal Group SO (3) as a solution to the attitude filtering problem. One of the most common potential functions for nonlinear deterministic attitude observers is studied and reformulated to address the noise attached to the attitude dynamics. The resultant estimator and correction factor demonstrate convergence properties and remarkable ability to attenuate the noise. The stochastic dynamics of the attitude problem are mapped from SO (3) to Rodriguez vector. The proposed stochastic filter evolved on SO (3) guarantees that errors in the Rodriguez vector and estimates steer very close to the neighborhood of the origin and that the errors are semi-globally uniformly ultimately bounded in mean square. Simulation results illustrate the robustness of the proposed filter in the presence of high uncertainties in measurements.

Keywords:Robotics, Hybrid systems, Observers for nonlinear systems Abstract: Existence of disturbances in unknown environments is a pervasive challenge in robotic locomotion control. Disturbance observers are a class of unknown input observers that have been extensively used for disturbance rejection in numerous robotics applications. In this paper, we extend a class of widely used nonlinear disturbance observers to underactuated bipedal robots, which are controlled using hybrid zero dynamics-based control schemes. The proposed hybrid nonlinear disturbance observer provides the autonomous biped robot control system with disturbance rejection capabilities, while the underlying hybrid zero-dynamics based control law remains intact.

Keywords:Networked control systems, Control of networks, Network analysis and control Abstract: State-dependent networked dynamical systems are ones where the interconnections between agents change as a function of the states of the agents. Such systems are highly nonlinear, and a cohesive strategy for their control is lacking in the literature. In this paper, we present two techniques pertaining to the density control of such systems. Agent states are initially distributed according to some density, and a feedback law is designed to move the agents to a target density profile. We use optimal mass transport to design a feedforward control law propelling the agents towards this target density. Kernel density estimation, with constraints imposed by the state-dependent dynamics, is then used to allow each agent to estimate the local density of the agents.

Keywords:Networked control systems, Switched systems, Computational methods Abstract: Along with the forth industry revolution, implementing industrial control systems over mainstream wireless networks such as WirelessHART, WiFi, and cellular networks becomes necessary. Well-known challenges, such as uncertain time delays and packet drops, induced by networks have been intensively investigated from various perspectives: control synthesis, network design, or control and network co-design. The status quo is that industry remains hesitant to close the loop at the control-to-actuation side due to safety concerns. This work offers an alternative perspective to address the safety concern, by exploiting the design freedom of system architecture. Specifically, we present a smart actuation architecture, which deploys (1) a remote controller, which communicates with physical plant via wireless network, accounting for optimality, adaptation, and constraints by conducting computationally expensive operations; (2) a smart actuator, which co-locates with the physical plant, executing a local control policy and accounting for system safety in the view of network imperfections. Both the remote and the local controllers run at the same time scale and cooperate through an unreliable network. We propose a policy iteration-based procedure to co-design the local and remote controllers when the latter employs the model predictive control policy. Semi-global asymptotic stability of the resulting closed-loop system can be established for certain classes of plants. Extensive simulations demonstrate the advantages of the proposed architecture and co-design procedure.

Keywords:Networked control systems, Control over communications, Distributed control Abstract: Consensus algorithms constitute a powerful tool for computing average values or coordinating agents in many distributed applications. Unfortunately, the same property that allows this computation (i.e., the nontrivial nullspace of the state matrix) leads to unbounded state variance in the presence of measurement errors. In this work, we explore the trade-off between relative and absolute communication (feedback) in the presence of measurement errors. We evaluate the robustness of first and second order integrator systems under a parametrized family of controllers (homotopy) that continuously trade between relative and absolute feedback interconnections in terms of the H2 norm an appropriately defined input-output system. Our approach extends previous H2 norm based analysis to systems with directed feedback interconnections whose underlying weighted graph Laplacians are diagonalizable. Our results indicate that any level of absolute communication is sufficient to achieve a finite H 2 norm but that purely relative feedback can only achieve finite norms when the measurement error is not exciting subspace associated with the consensus state. Numerical examples demonstrate that smoothly reducing the proportion of relative feedback in double integrator systems smoothly decreases the system performance and that this performance degradation is more rapid systems with relative feedback in only the first state (position).

Keywords:Networked control systems, Robust adaptive control, Constrained control Abstract: In this work, we present a new approach to design event-triggered adaptive control for a class of uncertain nonlinear systems with guaranteed performance. A prescribed performance function, which is characterized with the convergence rate, maximum overshoot, and steady error, is utilized to convert the original tracking error into a new error variable, resulting in a transformed error dynamic model. By designing event-triggered control for the transformed error dynamic model, the corresponding control scheme is able to ensure prescribed performance and reduce communication burden simultaneously. Simulation verification also confirms the effectiveness of the proposed approach.

Keywords:Networked control systems, Control over communications, Linear systems Abstract: This paper investigates robustness in first and second order integrator networks subject to distributed disturbances in terms of the collision potential of critical node pairs. Our results extend previous analysis quantifying this notion of robustness using an L_2 to L_infinity norm in networks with symmetric feedback interconnection to systems with directed feedback structures. We focus on the special case where the underlying feedback interconnection is represented by strongly connected digraph described by a diagonalizable weighted graph Laplacian matrix. We then exploit the fact that the L_2 to L_infinity norm can be computed as the H_2 norm of the system with an appropriately defined input-output pair to derive analytical expressions for the system robustness for first and second order systems with various combinations of absolute and relative state feedback. Finally, we perform numerical studies for a second order system connected over a line graph (vehicle platoon) to investigate the effect of asymmetric feedback control laws on performance and discuss how this compares to the stability margin improvements these control laws are known to provide in this application. Our results show that in contrast to the previous results on stability, asymmetric feedback control laws can increase the collision potential of certain vehicle pairs in platoons with and without leaders.

Keywords:Agents-based systems, Cooperative control, Networked control systems Abstract: We develop and analyze a distributed nonlinear iterative algorithm that enables the components of a multi-component system, each with some integer initial value, to asymptotically reach average consensus on their initial values, without having to reveal to other components the specific value they contribute to the average calculation. In particular, we assume an arbitrary communication topology captured by a strongly connected digraph, in which certain nodes (components) might be curious but not malicious (i.e., they execute the proposed protocol correctly, but try to identify the initial values of other nodes). We first discuss how a distributed algorithm that operates exclusively on integer values can be used to obtain the average of the node values. We then describe how this algorithm can be adjusted using homomorphic encryption to allow the nodes to obtain the average of their initial values while ensuring their privacy, at least assuming the presence of a trusted node.

Keywords:Observers for nonlinear systems, Lyapunov methods, Estimation Abstract: This Tutorial aims at providing an introduction and perspective on new concepts for the growing field of observer design for systems with symmetry. We will consider the design of computationally tractable state observer algorithms for the class of nonlinear systems for which the observer state can be represented as an element of a mathematical structure known as a Lie group and whose kinematics and dynamics respect this structure. Most autonomous robots can be modelled this way due to the symmetry of the physical laws that underpin their dynamics. There is a wide class of robotic applications for which this is the case and the theory developed is finding substantial application. The tutorial provides a range of perspectives on observer design for symmetric systems, including Lyapunov and gradient design methods for Luenberger type observers. Interested readers are referred to R.E. Mahony, J. Trumpf, T. Hamel. Observers for Kinematic Systems with Symmetry. In Proceedings of the 2013 IFAC NOLCOS Symposium.

Keywords:Observers for nonlinear systems, Lyapunov methods, Estimation Abstract: Many physical systems, and most mobile robotic vehicles, have physical models with symmetries that encode the in- variance of the laws of motion. That is, the behaviour of the system at one point in space is the same as its behaviour at another point in space, at least when viewed through a symmetric transformation of space. Such structure is of particular importance in the design of observers: if a stable high performance observer can be constructed at one point in space, then it can also be transported to all points in space to obtain a global observer design. Observers designed using this principle are known as equivariant observers and the approach offers considerable benefits in design methodology and error stability analysis. This talk will motivate the underlying class of systems for which equivariant observers can be constructed, the class of kinematic systems with complete symmetry. A range of motivating examples will be introduced including the original motivating applications of attitude estimation for aerial vehicles, as well as pose estimation applications that are now integral in head pose trackers for augmented reality systems, homography estimators used in visual servo control, and through to recent applications in Simultaneous Localisation and Mapping (SLAM). I will show how the observer dynamics are naturally posed on a Lie group that forms the symmetry space for the problem.

Keywords:Observers for nonlinear systems, Lyapunov methods, Estimation Abstract: In this part, we consider observer synthesis using Lyapunov design principles. We begin with cost functions on the outputs that can be realized from available measurements. By imposing invariance on the costs we can lift these costs to a non-degenerate cost in the error coordinates. For an actual design problem, the simplest approach at this point is to undertake a direct Lyapunov design process and we provide examples to demonstrate how this can be done. In more generality, we show how the cost can be used to define an equivariant gradient innovation once an invariant metric on the Lie group is defined. This construction leads to a gradient flow in the error coordinates that is straightforward to analyze for stability. We also provide the intuition and the main formulas required to extend the proposed design methodology to an observer that also estimates either an unknown constant bias offset in the measured velocity or a time-varying bias based on an internal model. Finally, we provide experimental evidence of the performance of the observer design methodology on different practical examples.

Keywords:Algebraic/geometric methods, Observers for nonlinear systems, Aerospace Abstract: In this tutorial paper, we discuss the design of geometric observers on Lie groups in the presence of noise. First we review Lie groups, and the mathematical definition of noises on Lie groups, both in discrete and continuous time. In particular, we discuss the Ito-Stratonovich dilemma. Then, we review the recently introduced notion of group affine systems on Lie groups. For those systems, we discuss how using the machinery of Harris chains, (almost) globally convergent deterministic observers might be shown to possess stochastic properties in the presence of noise. We also discuss the design of (invariant) extended Kalman filters (IEKF), and we recall the main result, i.e., the Riccati equation computed by the filter to tune its gains has the remarkable property that the Jacobians (A,C) with respect to the system's dynamics and output map are independent of the followed trajectory, whereas the noise covariance matrices that appear in the Riccati equation may depend on the followed trajectory. Owing to this partial independence, some local deterministic convergence properties of the IEKF for group-affine systems on Lie groups may be proved under standard observability conditions.

Keywords:Algebraic/geometric methods, Observers for nonlinear systems, Stability of nonlinear systems Abstract: Stable estimation of rigid body motion states from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange-d’Alembert principle from variational mechanics. From body-fixed sensor measurements, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in velocity estimation errors and an artificial potential function of pose (attitude and position) estimation errors. An additional dissipation term that is linear in the velocity estimation errors is introduced, and the Lagrange-d’Alembert principle is applied to the Lagrangian with this dissipation. This estimation framework is shown to be almost globally asymptotically stable in the state space of rigid body motions. It is discretized for computer implementation using the discrete Lagrange-d’Alembert principle, as a first order Lie group variational integrator. In the presence of bounded measurement noise from sensors, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states. Ongoing and future work will explore finitetime stable extensions of this framework for nonlinear observer design, with applications to rigid body and multi-body systems.

Keywords:Observers for nonlinear systems, Algebraic/geometric methods Abstract: This paper provides a new perspective on the structure of kinematic systems with complete symmetry. These systems naturally occur as models for mechanical systems with symmetry, for example flying or submersible robots. The configuration space of such systems is a homogeneous space of the symmetry Lie group, and it is well known that their kinematics can be lifted to equivariant kinematics on the symmetry group thus allowing global state observer constructions. We provide explicitly checkable sufficient differential-algebraic conditions on the symmetry that will lead to a lifted system in the form of standard left or right invariant kinematics on the symmetry group. Previously known conditions for one of these two cases required finding a velocity lift map with particular properties for which there was no general construction known.

Keywords:Cooperative control, Variable-structure/sliding-mode control, Optimal control Abstract: In this paper, a cooperative distributed optimization method via sliding mode extremum seeking (ES) control for a class of large-scale interconnected systems is presented. In this approach, a consensus algorithm is exploited to communicate the value of the global cost function to the ES controllers. Then, each sliding mode ES controller is designed such that a multivariable cost function is optimized in a cooperative fashion. The stability and convergence conditions for the ES controllers are determined and sufficient conditions for the distributed scheme to converge to the vicinity of the optimal points are driven. The application of the proposed scheme to a real-world example is investigated and simulations are provided to illustrate the theoretical results and demonstrate their potential use.

Keywords:Cooperative control, Autonomous systems, Agents-based systems Abstract: This paper studies the stability of equilibria of a nonlinear opinion dynamics model proposed in [1] for biased assimilation, which generalizes the DeGroot model by introducing a bias parameter. When the bias parameter is zero, the model reduces to the original DeGroot model. A positive value of this parameter reflects the degree of how biased an agent is. The opinions of the agents lie between 0 and 1. When the bias parameter is positive, it is shown that the equilibria with all elements equal identically to the extreme value 0 or 1 is locally stable, while the equilibrium with all elements equal to the intermediate consensus value 1/2 is unstable. For the equilibrium consisting of both extreme values 0 and 1, which corresponds to opinion polarization according to the model, it is shown that the equilibrium is locally stable if the bias parameter is greater than one for two-island networks, becomes unstable if the bias parameter is less than one, and its stability heavily depends on the network topology when the parameter equals one, in which case the limiting behavior of the model is established for certain initial conditions. It is also shown that for a small negative bias parameter, with which the agents can be regarded as anti-biased, the equilibrium with all elements equal to 1/2 is locally stable.

Keywords:Cooperative control, Distributed control, Sampled-data control Abstract: This paper studies discrete-time attitude synchronization for a group of networked rigid bodies in three dimensions. The challenge is how to deal with 3-D attitude motion dynamics on the Special Orthogonal group: SO(3) in the discrete-time domain, and it is rigorously considered by employing exponential mapping. The rigid body network consisting of multiple bodies with discrete-time attitude dynamics, relative attitude measurements, and directed interconnection topology between the bodies is first defined. Attitude synchronization is next defined as the goal for the rigid body network. Then, as the main feature of this work, it is newly shown that each attitude dynamics has a passivity shortage property, and novel distributed attitude synchronization laws based on the property are proposed. Convergence analysis and simulation verification show the validity of the present approach.

Keywords:Cooperative control, Networked control systems, Autonomous robots Abstract: A distributed coverage control strategy is developed for a group of heterogeneous robots in this work. Most existing coverage controllers assume the relation between the underlying density function and the locations of the robots is independent. To relax the condition for more potential applications, a new coverage control strategy that accounts for the dependence between the underlying density function and the locations of the robots is developed, and moreover, it can be extended to the conventional coverage controller by selecting specific system parameters. In addition, the heterogeneity among the robots can also cause various levels of reduction to the underlying density function, and hence, an Enhanced Multiplicatively Weighted Voronoi (EMWV) partition along with the controller is developed, so that optimal coverage can be obtained despite the heterogeneity between the robots. Stability analysis is proven to ensure system convergence, and simulations are conducted to verify the efficacy of the developed controllers.

Univ. of New South Wales at the AustralianDefenceForceAcad

Keywords:Cooperative control, Uncertain systems, Lyapunov methods Abstract: In this paper, a combined formation acquisition and cooperative extremum seeking control scheme is proposed for a team of three robots moving on a plane. The extremum seeking task is to find the maximizer of an unknown two dimensional function on the plane. The function represents the signal strength field due to a source located at the maximizer, and is assumed to be locally concave around the maximizer and monotonically decreasing in distance to the source location. Taylor expansions of the field function at the location of a particular lead robot and the maximizer are used together with a gradient estimator based on signal strength measurements of the robots to design and analyze the proposed control scheme. The proposed scheme is proven to exponentially and simultaneously (i) acquire the specified geometric formation and (ii) drive the lead robot to a specified neighbourhood disk around the maximizer, whose radius depends on the specified desired formation size as well as the norm bounds of the Hessian of the field function. The performance of the proposed control scheme is evaluated using a set of simulation experiments.

Keywords:Control of networks, Distributed control, Sampled-data control Abstract: This paper studies consensus control of linear multi-agent systems (MASs) over directed graphs. The communication topology is assumed to be strongly connected. A distributed event-triggered state-feedback protocol is proposed for achieving consensus, which monitors the relative state information between neighboring agents and triggers a sampling event when some state-related inequalities are violated. An existence condition for the protocol is derived, which needs to solve an algebraic Riccati equation and find some scalar parameters related to the graph Laplacian. It is proved that the protocol excludes both singular triggering behavior and Zeno behavior if some scalars are properly assigned. Compared with the existing results, the proposed method can deal with general linear MASs on strongly connected graphs but does not require the absolute state information of agents. The effectiveness of the proposed method is illustrated by a numerical example.

Keywords:Distributed parameter systems, Sensor networks, Estimation Abstract: This work incorporates the effects that hazardous environments have on sensing devices, in the guidance of mobile platforms with onboard sensors. Mobile sensors are utilized in the state reconstruction of spatiotemporally varying processes, often described by advection-diffusion PDEs. A typical sensor guidance policy is based on a gradient ascent scheme which repositions the sensors to spatial regions that have larger state estimation errors. If the cumulative measurements of the spatial process are used as a means to represent the effects of hazardous environments on the sensors, then the sensors are considered inoperable the instance the cumulative measurements exceed a device-specific tolerance level. A binary guidance policy considered earlier repositioned the sensors to regions of larger values of the state estimation errors thus implementing an information-sensitive policy. The policy switched to an information-averse guidance the instance the cumulative effects exceeded a certain tolerance level. Such a binary policy switches the sensor velocity abruptly from a positive to a negative value. To alleviate these discontinuity effects, a ternary guidance policy is considered and which inserts a third guidance policy, the information-neutral policy, that smooths out the transitions from information-sensitive to information-averse guidance. A novelty in this ternary guidance has to do with the level-set approach which changes from a guidance towards large values of the state estimation error towards level sets of the state estimation error and eventually towards reduced values of the state estimation error. An example on an advection-diffusion PDE in 2D employing a single interior mobile sensor using both the binary and ternary guidance policies is used to demonstrate the effects of hazardous environments on both the sensor life expectancy and the performance of the state estimator.

Keywords:Modeling, Distributed parameter systems, Uncertain systems Abstract: When modeling dynamical systems with uncertainty, one usualy resort to stochastic calculus and, specifically, Brownian motion. Recently, we proposed an alternative approach based on time-evolution of measures, called Measure Differential Equations, which can be seen as natural generalization of Ordinary Differential Equations to measures. The approach allows to pass to the limit in discrete approximations and attain finite-speed diffusion, concentration and other phenomena. In this paper we start building the theory of Measure Differential Inclusions which are the counterpart of Differential Inclusions for measures. We provide the general definitions and prove existence of solutions under continuity and convexity properties.

Keywords:Distributed parameter systems, Autonomous systems Abstract: This paper considers scenarios wherein a hacker hacks into a subset of UAVs in a swarm and turns them into vehicles with malicious intent. The objective of the malicious vehicles is to prevent the swarm from performing its intended mission, and thereby compromise the effectiveness of the overall swarm. The two species of UAVs in the swarm - malicious UAVs and normal UAVS, as well as their associated interaction effects, are modeled using Partial Differential Equations (PDEs). The malicious UAVs choose a reference density profile of the normal UAVs which, when enforced, would reduce the effectiveness of the swarm. The malicious UAVs then perform a sequence of velocity changes with the objective of changing the density profile of the normal UAVs so that it tracks the reference density profile. Analytical expressions governing the velocity inputs of the malicious vehicles with which they can generate such density changes in the normal UAVs, are demonstrated. Simulations are presented to demonstrate the working of the attack model.

Keywords:Distributed parameter systems, Observers for Linear systems, Switched systems Abstract: The pointwise expected value of the solution of a randomly switching reaction-diffusion PDE is by itself the solution of a deterministic system of coupled reaction-diffusion equations; provided that the random switching is Markovian and that the PDE satisfies some regularity conditions. Following recent results on boundary observers for systems of coupled reaction-diffusion equations, an observer is constructed for the asymptotic estimation of the expected value of the randomly switching reaction-diffusion PDE. Although only the case where the PDE switches between two states is developed here, the same results hold for an arbitrary, but finite, number of switching states. In general, the observer gains are to be computed numerically from the solution of a system of coupled second order hyperbolic PDEs. Several phenomena described by randomly switching reaction-diffusion PDEs, for example: neurotransmitters diffusion that take into account switching between quiescent and firing states, thermostats and failure in lithium-ion batteries.

Keywords:Distributed parameter systems, Distributed control, Stochastic systems Abstract: In this paper, we generalize our diffusion-based approach [1] to achieve coverage of a bounded domain by a robotic swarm according to a target probability density that is a function of a locally measurable scalar field. We generalize this approach in two different ways. First, we show that our method can be extended in a natural way to scenarios where the robots' state space is a compact Riemannian manifold, which is the case if the robots are confined to a surface or if their configuration space is non-Euclidean due to dynamical constraints such as those present in most mechanical systems. Then, we establish the stability properties of a weighted variation of the porous media equation, a nonlinear partial differential equation (PDE). Coverage strategies based on these nonlinear PDEs have the advantage that the robots stop moving once the equilibrium probability density is reached, in contrast to our original approach [1]. We establish long-time stability properties of the target probability densities using semigroup theoretic arguments. We validate our theoretical results through stochastic simulations of a linear diffusion-based coverage strategy on a 2-dimensional sphere and numerical solutions of the weighted porous media equation on the 2-dimensional torus.

[1] Karthik Elamvazhuthi, Chase Adams, and Spring Berman. Coverageand field estimation on bounded domains by diffusive swarms. InIEEEConf. on Decision and Control (CDC), pages 2867–2874. IEEE, 2016

Keywords:Distributed control, Distributed parameter systems Abstract: This paper presents the design of an exponentially stabilizing controller for a one-dimensional wave partial differential equation (PDE). The control is acting on a Robin's boundary condition while the opposite boundary satisfies an unstable dynamic. The wave is also subject to unstable in-domain source terms. Closed-loop exponential stabilization is obtained via a full-state backstepping controller. The existence and uniqueness of this backstepping transformation is proven, using the method of successive approximations.

Keywords:Observers for nonlinear systems, Estimation, Vision-based control Abstract: For some problems, such as monocular visual odometry (VO), vector measurements are given with unknown magnitude. In VO, the magnitude can be found by recognizing features with known position, or with an extra sensor such as an altimeter. This article presents a nonlinear observer that uses the derivative of the vector as an additional measurement for estimating the magnitude of a vector. For the VO example, this means that the velocity can be estimated by fusing the normalized velocity vector with acceleration measurements. The observer exploits the fact that the dynamics of the normalized vector is dependent on the magnitude of the vector. The observer employs methods from nonlinear/adaptive estimation; filters the unit vector on the unit sphere, and retrieves the magnitude of the vector. The observer is shown to be uniformly semi-globally asymptotically stable and uniformly locally exponentially stable. The observer is applied to the bearing-only SLAM filter problem as an example.

Keywords:Observers for nonlinear systems, Distributed parameter systems, Lyapunov methods Abstract: Considering a class of hyperbolic systems of balance laws with distributed measurements, and possibly distributed effects of known inputs, a structure suitable for uniform observability is first emphasized. Sufficient conditions for an explicit high-gain observer design are then derived for special cases of such systems. The stability of the related observer estimation error is fully established by means of Lyapunov-based techniques, and a numerical example finally illustrates the results.

Keywords:Observers for nonlinear systems, Stability of hybrid systems, Aerospace Abstract: This paper considers the problem of orientation, position and linear velocity estimation for a rigid body navigating in 3D space. We propose a globally exponentially stable (GES) nonlinear hybrid observer, designed on the matrix Lie group SE_2(3), relying on an inertial measurement unit (IMU) and landmark measurements. A rigorous stability analysis has been provided based on the framework of hybrid dynamical systems. Simulation results are presented to illustrate the performance of the proposed hybrid observer.

Keywords:Observers for nonlinear systems, Algebraic/geometric methods Abstract: The paper addresses the problem of transforming single-output continuous and discrete-time nonlinear dynamical systems into their respective extended observer forms. The output injection term in the extended observer form of degree l depends, besides on the output also on its first l derivatives (in the continuous-time case) or first l past values (in the discrete-time case). Intrinsic necessary and sufficient conditions are given for the existence of the state transformation that transforms the equations into the extended observer form, both for continuous- and discrete-time cases. The conditions can be directly checked from state equations and do not rely on the input-output equation as in the earlier papers.

Keywords:Observers for nonlinear systems, Cooperative control, Autonomous systems Abstract: We consider a spatial vector field estimation problem with vehicles modeled as unicycles. The vector field is assumed to affect the motion of the vehicles in an additive fashion. We investigate whether the position information of the vehicles can be used to simultaneously estimate the unknown field parameters and the heading information of the vehicles. Starting with a single vehicle case, we design a stable nonlinear observer and reveal a persistence of excitation (PE) condition on the vehicle’s motion that guarantees the convergence of the field parameter estimates and the heading estimates almost globally. We next extend the observer for multiple vehicles with a strongly connected communication topology and provide a PE condition to ensure filter convergence. The effectiveness of the designed observers is demonstrated with simulations of vehicles estimating a rotational field.

Keywords:Observers for nonlinear systems, Aerospace, Sensor fusion Abstract: This paper considers the problem of attitude estimation for rigid bodies using measurements from a triaxial rate gyro and two other vector sensors (e.g. accelerometers, magnetometers). The novelty is to take into account biases not only on the gyro, but also on one of the vector measurements. The attitude estimation is achieved by a nonlinear, ``geometry-free'', observer. We also study the observability of the system and obtain conditions under which the reconstruction of both the attitude and the biases is possible. Under these persistency-of-excitation conditions, and through an explicit Lyapunov analysis, we then establish the global asymptotic and local exponential convergence of the observer. The theoretical results are illustrated by a thorough numerical simulation.

Keywords:Adaptive control, Hybrid systems, Linear systems Abstract: In this paper we propose an adaptive regulator for general multivariable linear systems to deal with references and disturbances generated by an unknown exosystem. The proposed regulator merges a continuous-time internal model and a discrete-time least-squares identifier that adapts the internal model parameters. We show that, under a suitable persistence of excitation condition, asymptotic regulation is achieved whenever an upper bound on the dimension of the exosystem is known.

Keywords:Adaptive control, Cooperative control, Stochastic systems Abstract: In this paper, we develop a distributed robust adaptive control architecture for addressing networked multiagent systems subject to agent model uncertainty, exogenous stochastic disturbances, and compromised sensor and actuators. Specifically, for a class of linear leader-follower multiagent uncertain systems, we develop a robust adaptive control design protocol for each follower. The proposed adaptive controller guarantees uniform ultimate boundedness of the state tracking error for each agent in a mean-square sense.

Keywords:Adaptive systems, Estimation, Identification Abstract: This paper contributes to the solution of adaptive tracking issues adopting Bayesian principles. The incomplete model of parameter variations is substituted by relaying on the use of data-suppressing procedure with two goals pursued: to provide automatic memory scheduling through the data-driven forgetting factor, and to compensate for the potential loss of persistency. The solution we propose is the geometric mean of the posterior probability density function (pdf) and its proper alternative, which, for the normal distribution, can be reduced to the convex combination of the information matrix and its regular counterpart. This coupling policy results from maximin decision-making, where the Kullback-Leibler divergence (KLD) occurs as a measure of discrepancy. In this context, the weight (probability) assigned to the information matrix is regarded as the forgetting factor and is controlled by a globally convergent Newton algorithm.

Keywords:Adaptive control, Adaptive systems, Cooperative control Abstract: This paper considers the problem of composite consensus control and cooperative adaptive learning of a class of linear uncertain multi-agent systems (MASs). The objective is to jointly achieve leader-following consensus tracking and accurate identification of unknown system parameters for all follower agents. A new cooperative adaptive consensus control protocol is proposed, which consists of a discontinuous nonlinear state-feedback control law and a series of filters for cooperative adaptation. Attractiveness of this new protocol lies in its utilization of not only relative plant state information but also relative estimate parameter information. The consensus and learning performance is rigorously analyzed using Lyapunov function approach. It is shown that exponential convergence of both consensus tracking errors to zero and adaptation parameters to their true values can be achieved simultaneously under a mild cooperative finite-time excitation (cFTE) condition. This cFTE condition significantly relaxes many existing excitation conditions (e.g., persistent excitation) for exponential parameter convergence in adaptive control systems. A numerical example is used to demonstrate the proposed approach.

Keywords:Adaptive control, Control of networks, Chaotic systems Abstract: In this paper, we address the problem of finite time adaptive synchronization of two-layer networks, and take the effect of stochastic perturbation into consideration. By adopting the integrated control protocols including a finite-time controller and an adaptive controller, sufficient conditions for realizing synchronization of two-layer networks with identical and nonidentical topologies are derived based on the finite-time stability theory of (stochastic) differential equations. Besides, a wide range of finite-time adaptive synchronization in multilayer networks can be achieved under the proposed strategies. Finally, the classical Chen system and Lorenz system are taken as the examples of node dynamics to illustrate the effectiveness and feasibility of the theoretical results.

Keywords:Adaptive control, Robust adaptive control, Flight control Abstract: In classical model reference adaptive control, the closed-loop system’s ability to track a given reference signal can be tuned by choosing the adaptive rates and parameterizing the solution of an algebraic Lyapunov equation that appears in the adaptive law. The projection operator can be employed to impose user-defined constraints on the adaptive gains. However, using the projection operator and quadratic Lyapunov functions to certify uniform ultimate boundedness of the trajectory tracking error, the bounds on the trajectory tracking error can only be estimated, but not explicitly imposed a priori. In this paper, we provide an adaptive control law for the same class of nonlinear dynamical systems as classical model reference adaptive control. A barrier Lyapunov function guarantees that user-defined constraints on both the trajectory tracking error and the adaptive gains are verified.

Keywords:Identification, Learning, Optimization Abstract: We consider the problem of learning graphical models where the support of the concentration matrix can be decomposed as a Kronecker product. We propose a method that uses the Bayesian hierarchical learning modeling approach. Thanks to the particular structure of the graph, we use a the number of hyperparameters which is small compared to the number of nodes in the graphical model. In this way, we avoid overfitting in the estimation of the hyperparameters. Finally, we test the effectiveness of the proposed method by a numerical example.

Keywords:Identification, Numerical algorithms Abstract: The practical utility of system identification algorithms is often limited by the reliability of their implementation in finite precision arithmetic. The aim of this paper is to develop a method for the numerically reliable identification of fast sampled systems. In this paper, a data-dependent orthonormal polynomial approach is developed for systems parametrized in the delta-domain. This effectively addresses both the numerical conditioning issues encountered in frequency-domain system identification and the inherent numerical round-off problems of fast-sampled systems in the common Z-domain description. Superiority of the proposed approach is shown in an example.

Keywords:Identification, Estimation, Linear systems Abstract: The model identification problem for asymptotically stable linear time invariant systems is considered. The system output is affected by an additive noise with unknown bound, and a finite set of data is available for parameter estimation. The goal is to derive a model with guaranteed simulation error bounds for all predicted time steps, up to a finite horizon of choice. This is achieved in three steps. At first, the noise bound, system order, and impulse response decay rate are estimated from data. Then, the estimated quantities are used to refine the sets of all possible multi-step predictors compatible with data and prior assumptions (Feasible Parameter Sets, FPSs). The FPSs allow one to derive, in a Set Membership framework, guaranteed error bounds for any given multi-step predictor, including the one obtained by simulating the system model. Finally, the wanted model parameters are identified by numerical optimization, imposing the constraints provided by the FPSs and using one of two proposed optimality criteria. Numerical simulations illustrate the validity of the approach.

Keywords:Identification, Simulation, Nonlinear systems identification Abstract: In this paper, we show that the common approach for simulation non-linear stochastic models, commonly used in system identification, via setting the noise contributions to zero results in a biased response. We also demonstrate that to achieve unbiased simulation of finite order NARMAX models, in general, we require infinite order simulation models.The main contributions of the paper are two-fold. Firstly, an alternate representation of polynomial NARMAX models, based on Hermite polynomials, is proposed. The proposed representation provides a convenient way to translate a polynomial NARMAX model to a corresponding simulation model by simply setting certain terms to zero. This translation is exact when the simulation model can be written as an NFIR model. Secondly, a parameterized approximation method is proposed to curtail infinite order simulation models to a finite order. The proposed approximation can be viewed as a trade-off between the conventional approach of setting noise contributions to zero and the approach of incorporating the bias introduced by higher-order moments of the noise distribution. Simulation studies are provided to illustrate the utility of the proposed representation and approximation method.

Keywords:Identification, Subspace methods, Linear systems Abstract: This paper introduces a data-driven method for determining the order of the partial difference equation of a discrete two dimensional (2D) linear system. A Hankel matrix (referred to as recursive Hankel matrix) is constructed from the available two dimensional data in a recursive way. This method of data Hankelization can be represented by a moving window that slides over the data. This paper extends the concept of past and future data to 2D systems and introduces the concept of left, right, top and bottom data. It is shown that the intersection between left, right, top and bottom Hankel matrices reveals the order of the underlying linear 2D system. As an example, we applied the method to data generated by a discretized transport diffusion equation. Our method correctly estimated the order of the difference equation.

Keywords:Identification, Estimation, Optimization Abstract: In this paper we propose an acoustic source identification algorithm to localize multiple sources in non-trivial domains. We capture the physics of the acoustic wave propagation via the Helmholtz partial differential equation. Given a set of noisy complex pressure measurements of an acoustic field, we formulate an optimization problem to solve for the locations, shapes, and intensities of the sources that minimize the discrepancy between the observed pressure measurements and those predicted by the model. We parametrize each source with a nonlinear function that depends on a small set of parameters, greatly reducing the dimension of the problem. We present an initialization method for the resulting nonlinear optimization problem. We present experimental results showing the ability of our method to correctly identify multiple acoustic sources in a free field domain as well as a domain with obstacles and reflecting boundaries. Moreover, we show that our method can identify more interesting properties of the source field, such as relative phase difference between sources.

Keywords:Estimation, Kalman filtering, Distributed control Abstract: Covariance intersection (CI) extends Kalman filter (KF) in distributed estimation, since it can fuse Gaussian estimates in the absence of the estimates' correlations. However, even with the preliminary success on the integration of CI and KF, existing discussion limited in global behavior is unable to directly deal with a system with a mixture of unbounded-covariance and bounded-covariance agents. In other words, until this paper there has been no explicit investigation on the analytic relationship between effective observability in each agent and system topology, to the best of our knowledge. To formalize these problems, we establish CI-based KF with explicit CI topology, on top of the conventional KF with observation exchanges. Consequently, the effect of CI on KF can be characterized by the impact of individual CI links on each agents. In particular, we systematically show that CI links can diminish the effective unobservable space, which relaxes the boundedness criterion. In addition, as a conservative fusion scheme, there may exist CI links that provide no improvement on estimation performance but generate additional uncertainty. A method is proposed to identify and then to suppress such redundant CI links for enhanced estimation performance. Finally, the pros and cons of CI on distributed estimation algorithms are comprehensively characterized and substantiated by a numerical example.

Keywords:Estimation, Grey-box modeling, Nonlinear systems identification Abstract: Many models have known structure but unknown parameters. Nonlinear estimation methods, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), and ensemble Kalman filter (EnKF) are typically applied to these problems by viewing the unknown parameters as constant states. An alternative approach is provided by retrospective cost model refinement (RCMR), which uses an error signal given by the difference between the output of the physical system and the output of the model to update the parameter estimate. The parameter update is based on the retrospective cost function, whose minimizer updates the coefficients of the estimator. The present paper extends RCMR to the case where the model depends nonlinearly on multiple unknown parameters.

Keywords:Estimation, Linear systems Abstract: In Cyber-Physical Systems (CPSs), inference based on communicated data is of critical significance as it can be used to manipulate or damage the control operations by adversaries. This calls for efficient mechanisms for secure transmission of data since control systems are becoming increasingly distributed over larger geographical areas. Distortion based security, recently proposed as one candidate for CPSs security, is not only more appropriate for these applications but also quite frugal in terms of prior requirements on shared keys. In this paper, we propose distortion-based metrics to protect CPSs communication and show that it is possible to confuse adversaries with just a few bits of pre-shared keys.

Keywords:Estimation, Numerical algorithms, Identification Abstract: This paper proposes a fast algorithm for the training of adaptive hinging hyperplanes (AHH), which is a popular and effective continuous piecewise afﬁne (CPWA) model consisting of a linear combination of basis functions. The original AHH incrementally generates new basis functions by simply traversing all the existing basis functions in each dimension with the pre-given knots. Meanwhile, it also incorporates a backward procedure to delete redundant basis functions, which avoids over-ﬁtting. In this paper, we accelerate the procedure of AHH in generating new basis functions, and the backward deletion is replaced with Lasso regularization, which is robust, requires less computation, and manages to prevent over-ﬁtting. Besides, the selection of the splitting knots based on training data is also discussed. Numerical experiments show that the proposed algorithm signiﬁcantly improves the efﬁciency of the existing AHH algorithm even with higher accuracy and it also enhances robustness in the given benchmark problems.

Keywords:Estimation, Observers for nonlinear systems, Aerospace Abstract: This paper considers the Simultaneous Localization and Mapping (SLAM) problem for a rigid body evolving in 3D space. We propose a nonlinear geometric observer, designed on the matrix Lie group SE_{1+n}(3), using group velocity and landmark measurements. The proposed observer is also extended to handle unknown biases in the linear and angular velocity. Simulation results are presented to illustrate the effectiveness of the proposed observer.

Keywords:Pattern recognition and classification, Observers for Linear systems, Estimation Abstract: We consider the problems of tracking an ensemble of indistinguishable agents with linear dynamics based only on output measurements. In this setting, the dynamics of the agents can be modeled by distribution flows in the state space and the measurements correspond to distributions in the output space. In this paper we formulate the corresponding state estimation problem using optimal mass transport theory with prior linear dynamics, and the optimal solution gives an estimate of the state trajectories of the ensemble. For general distributions of systems this can be formulated as a convex optimization problem which is computationally feasible when the number of state dimensions is low. In the case where the marginal distributions are Gaussian, the problem is reformulated as a semidefinite programming problem and can be efficiently solved for tracking systems with a large number of states.

Max Planck Institute for Dynamics of Complex Systems

Keywords:Lyapunov methods, Stability of nonlinear systems, Nonholonomic systems Abstract: In this paper, we propose a new control design scheme for solving the obstacle avoidance problem for nonlinear driftless control-affine systems. The class of systems under consideration satisfies controllability conditions with iterated Lie brackets up to the second order. The time-varying control strategy is defined explicitly in terms of the gradient of a potential function. It is shown that the limit behavior of the closed-loop system is characterized by the set of critical points of the potential function. The proposed control design method can be used under rather general assumptions on potential functions, and particular applications with navigation functions are illustrated by numerical examples.

Keywords:Vision-based control, Visual servo control, Lyapunov methods Abstract: This paper presents a new adaptive controller for homography-based visual servo tracking without using the derivative information of desired trajectory. Most of existing works require the measurement of desired trajectory derivative to provide feedforward component. However, this requirement leads to complicated off-line calculation, and the derivative measurement errors caused by image noises can degenerate the control performance. To avoid the aforementioned problems, an adaptive controller is developed based on the proposal of a derivative estimator of desired trajectory. Stability analysis is conducted by using Lyapunov-based techniques, demonstrating that both the tracking and estimation errors are uniformly ultimately bounded. Moreover, provided that the desired trajectory satisﬁes a certain condition, the proposed approach can achieve asymptotic tracking. The effectiveness of the proposed controller is validated by simulation results.

Keywords:Linear parameter-varying systems, Stability of linear systems, Lyapunov methods Abstract: New gridding-based algorithms for stability analysis of Linear Parameter-Varying (LPV) systems with general parameter dependencies are introduced. Recent results in Haar-based Lyapunov stability analysis allow to treat non-convex parametric domains and a large class of system parameter functions by using computationally implementable algorithms to solve the original infinite-dimensional and infinitely constrained problems, without requiring further checks even for arbitrarily sparse parameter grids. In contrast with previous theoretical results which are not constructive from the algorithmic and numerical point of view, the approach introduced here is systematic and amenable for practical implementation, avoiding complex analytical manipulations when a vast class of parameter dependencies is considered. Two numerical examples are used to validate the proposed algorithms.

Laboratoire Des Signaux Et Systemes, CNRS - SUPELEC

Keywords:Lyapunov methods, LMIs, Constrained control Abstract: We present sufficient conditions for the existence of periodic orbits of saturating planar systems. We characterize inner and outer sets bounding the periodic orbits. A method to build these bounds, based on the solution to a convex optimization problem, is proposed and illustrated with numerical examples.

Keywords:Lyapunov methods, Stability of nonlinear systems Abstract: In this paper we address the problem of self-triggered control of nonlinear systems under actuator delays. In particular, for globally asymptotically stabilizable systems we exploit the Lipschitz properties of the system's dynamics, and present a self-triggered strategy that guarantees the stability of the sampled closed-loop system with bounded actuator delays.

Keywords:Lyapunov methods, Stability of nonlinear systems Abstract: In this note we propose some families of differentiable strict Lyapunov functions (LFs) (whose derivative along the system's solutions is negative definite) for two classes of second-order systems. One of these classes arises in finite-time controlled systems, while the second class arises as observation error dynamics of finite-time observers. The design of the LFs is inspired by the fact that, for the considered systems, the construction of a weak (or non-strict) LF (whose derivative along the system's solutions is negative semidefinite) is relatively simple, and the LaSalle's conditions always hold to prove asymptotic stability at the origin. Then, the construction of strict LFs consists in transforming a weak LF into a strict one.

Keywords:Hybrid systems, Stability of hybrid systems, Aerospace Abstract: In this paper, we develop a hybrid controller for global asymptotic stabilization on the n-dimensional sphere (Sn) using synergistic potential functions. These consist of a collection of potential functions on Sn that induce a gradient descent controller during flows of the hybrid closed-loop system and a switching law that, at undesired equilibrium points of the gradient vector field, jumps to the lowest value among all the potential functions in the collection. We show that the proposed controller can be used for global reduced attitude synchronization, i.e., given a network of rigid-bodies, the proposed synergistic hybrid feedback can be used to globally synchronize a reference direction of each agent within a global but unknown inertial reference frame. We study this application for a network of three vehicles by means of simulation results.

Keywords:Hybrid systems, Computational methods Abstract: Signal Temporal Logic (STL) is a formal language for describing a broad range of real-valued, temporal properties in cyber-physical systems. While there has been extensive research on verification and control synthesis from STL requirements, there is no formal framework for comparing two STL formulae. In this paper, we show that under mild assumptions, STL formulae admit a metric space. We propose two metrics over this space based on i) the Pompeiu-Hausdorff distance and ii) the symmetric difference measure and present algorithms to compute them. Alongside illustrative examples, we present an application of these metrics as design quality measures where they are used to compare all the temporal behaviors of a designed system, such as a synthetic genetic circuit, with the "desired" specification.

Keywords:Hybrid systems, Optimization, Constrained control Abstract: This paper proposes an efficient encoding for Mixed Integer Quadratic Programming (MIQP) problems in optimally controlling constrained hybrid systems from an initial state into a target region over a finite time horizon. The set of admissible trajectories given the system semantics is formulated by tailored constraints involving binary variables to encode the transition dynamics. A subset of these constraints establish a phase sequencing, which reduces the number of possible value combinations for the binary variables significantly, resulting in lower computation times for solving the MIQP problem. An illustrating example demonstrates the low computation times.

Keywords:Hybrid systems, Stability of hybrid systems, Lyapunov methods Abstract: Many engineering systems require both continuous and discrete valued signals, as well as continuous and discrete time scales in their descriptions and are therefore known as hybrid systems. Recently, the concept of time-scale calculus was introduced as a unification of the theory of difference and differential equations, making it an ideal tool to analyze hybrid systems. The time-scale calculus can handle solutions of hybrid systems with infinitely many jumps. However, to date time-scale calculus restricts time to a non-empty closed subset of the real line which is not general enough to fully capture the dynamics of hybrid systems. A generalization is proposed to extend time-scale calculus such that the time can be defined on more suitable subsets of the real line. Stability definitions of hybrid systems using this framework are also introduced together with a Lyapunov characterization of global uniform stability. A few examples demonstrate the usefulness of this new framework.

Keywords:Hybrid systems, Switched systems, Discrete event systems Abstract: Regarding the eventuality property of a discrete-time affine system (DTAS), we investigate whether all trajectories in the system leave a given region. Based on the compactness of the region, this study is divided into two cases. For a compact region, we give an exact characterisation of the eventuality property. For a not necessarily compact region, we argue the verification problem can be converted to the evaluation of an invariant cone under a linear map. Finally we provide a sufficient condition for the eventuality property based on the knowledge of eigenvalues and generalized eigenvectors of a matrix. A computational evaluation of the analytical criteria is outlined.

Keywords:Hybrid systems, Embedded systems, Automata Abstract: Robust Linear Temporal Logic (rLTL) was crafted to incorporate the notion of robustness into Linear-time Temporal Logic specifications. Robustness is ubiquitous in control systems and translates the intuitive notion that "small" violations of environment assumptions should only lead to "small" violations of system guarantees. This notion was formalized in the logic rLTL via 5 different truth values and it led to an increase in the time complexity of the associated model-checking problem. In this paper we identify and analyze a fragment of rLTL for which the model checking problem can be solved using generalized Büchi automata with at most 3^{|φ|} states where |φ| denotes the length of an rLTL formula φ. This is a substantial improvement over the previously known bound of 5^{|φ|} and close to the tight upper bound 2^{|φ|} for LTL.

Keywords:Power systems, Smart grid, Optimization algorithms Abstract: This paper proposes an Automatic Power Exchange (APEX) that enables monetization of underutilized distribution system energy resources. APEX features an open-gate forward market design to incorporate uncertainty from variable resources, and an explicit flexibility market that schedules flexible resources based on information submitted by users through a simple yet expressive order format. We study the non-convex non-preemptive scheduling problem in APEX, proposing polynomial time algorithms with finite and asymptotic performance guarantees. We then analyze the properties of marginal pricing, generalized to fit the APEX context with forward markets and distribution network constraints. We establish that it is revenue adequate but may lead to inadmissible prices for flexible orders. We then suggest a simple pricing mechanism that provably produces admissible prices for users and adequate revenue for APEX if implemented together with the proposed scheduling algorithms.

Keywords:Power systems, Smart grid, Stability of nonlinear systems Abstract: Unstable equilibrium points are important for transient stability analysis of power systems since they can indicate the boundary of the region of attraction regarding a stable equilibrium point. This paper proposes a new holomorphic embedding method to find unstable equilibrium points for multi-generator power systems by solving an equivalent power flow problem considering generator speeds. The problem formulation and the proposed method are presented in detail and then verified on the IEEE 3-generator 9-bus power system with different parameters.

Keywords:Power systems, Lyapunov methods Abstract: We consider the problem of synchronizing two electric power generators, one of which (the leader) is serving a time-varying load, so that they can ultimately be connected to form a single power system. Both generators are described by second-order reduced state-space models, and we assume that the generator not serving any load initially (the follower) has access to measurements of the leader generator phase angle corrupted by some additive disturbances. By using these measurements, and leveraging results on reduced-order observers with ISS-type robustness, we propose a procedure that drives (i) the angular velocity of the follower close enough to that of the leader, and (ii) the phase angle of the follower close enough to that of the point at which both systems will be electrically connected. An explicit bound on the synchronization error in terms of the measurement disturbance and the variations in the electrical load served by the leader is computed. We illustrate the procedure via numerical simulations.

Keywords:Power systems, Hybrid systems, Predictive control for linear systems Abstract: As more non-synchronous renewable energy sources (RES) participate in power systems, the system's inertia decreases and becomes time dependent, challenging the ability of existing control schemes to maintain frequency stability. System operators, research laboratories, and academic institutes have expressed the importance to adapt to this new power system paradigm. As one of the potential solutions, virtual inertia has become an active research area. However, power dynamics have been modeled as time-invariant, by not modeling the variability in the system's inertia. To address this, we propose a new modeling framework for power system dynamics to simulate a time-varying evolution of rotational inertia coefficients in a network. We model power dynamics as a hybrid system with discrete modes representing different rotational inertia regimes of the network. We test the performance of two classical controllers from the literature in this new hybrid modeling framework: optimal closed-loop Model Predictive Control (MPC) and virtual inertia placement. Results show that the optimal closed-loop MPC controller (Linear MPC) performs the best in terms of cost; it is 82 percent less expensive than virtual inertia placement. It is also more efficient in terms of energy injected/absorbed to control frequency. To address the lower performance of virtual inertia placement, we then propose a new Dynamic Inertia Placement scheme and we find that it is more efficient in terms of cost (74 percent cheaper) and energy usage, compared to classical inertia placement schemes from the literature.

Keywords:Power systems, Stochastic systems, Computational methods Abstract: The frequency stability of power systems is increasingly challenged by various types of disturbance. In particular, the increasing penetration of renewable energy sources is increasing the variability of power generation while reducing system inertia against disturbances. In this paper we explore how this could give rise to rate of change of frequency (RoCoF) violations. Correlated and non-Gaussian power disturbances, such as may arise from renewable generation, have been shown to be significant in power system security analysis. We therefore introduce ghost sampling which, given any unconditional distribution of disturbances, efficiently produces samples conditional on a violation occurring. Our goal is to address questions such as "which generator is most likely to be disconnected due to a RoCoF violation?" or "what is the probability of having simultaneous RoCoF violations, given that a violation occurs?''

Swiss Federal Institute of Technology (ETH) Zurich

Keywords:Power systems, Optimization Abstract: Solutions to nonlinear, nonconvex optimization problems can fail to satisfy the KKT optimality conditions even when they are optimal. This is due to the fact that unless constraint qualifications (CQ) are satisfied, dual multipliers may fail to exist or may not be unique. This possibility also affects AC optimal power flow (OPF) problems which are routinely solved in power systems planning, scheduling and operations. The complex structure of the problems -- in particular the presence of the nonlinear power flow equations which naturally exhibit a structural degeneracy -- make any attempt to establish constraint qualifications for the entire class of problems very challenging. In this paper, we resort to tools from differential topology to show that for AC OPF problems in various contexts the linear independence constraint qualification is satisfied almost certainly, thus effectively obviating the usual assumption on CQs. Consequently, for any local optimizer there generically exists a unique set of dual multipliers that satisfies the KKT conditions.

Keywords:Optimization, Optimization algorithms, Control of networks Abstract: Optimization over Markov chains is a popular topic, since Markov chains can be used to model several important systems, such as telecommunications, railways or dams. However, most of the existing literature focuses on steady states and limiting distributions, while in some contexts it might be beneficial to design Markov chains with repulsive distributions, i.e., distributions that, once achieved, cause a large probability transition in the system. This, as typically done in Critical Infrastructure systems, corresponds to having resilient Markov chains that "spring back" after reaching potentially dangerous or unsafe configurations. In this paper we formulate a problem where we aim at redesigning a Markov chain in order from one side to maximize the repulsiveness of a prescribed distribution and from another side to minimize the redesign effort. In more detail, we formulate the problem as an optimization problem, and we provide a necessary and sufficient local optimality condition and a sufficient global optimality condition. We conclude the paper with simulations aimed at numerically demonstrating the theoretical findings in the paper.

Keywords:Optimization, Power systems Abstract: This paper is concerned with optimal power flow (OPF), which is the problem of optimizing the transmission of electricity in power systems. Our main contributions are as follows: (i) we propose a novel parabolic relaxation, which transforms non-convex OPF problems into convex quadratically-constrained quadratic programs (QCQPs) and can serve as an alternative to the common practice semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations, (ii) we propose a penalization technique which is compatible with the SDP, SOCP, and parabolic relaxations and guarantees the recovery of feasible solutions for OPF, under certain assumptions. The proposed penalized convex relaxation can be used sequentially to find feasible and near-globally optimal solutions for challenging instances of OPF. Extensive numerical experiments on small and large-scale benchmark systems corroborate the efficacy of the proposed approach. By solving a few rounds of penalized convex relaxation, fully feasible solutions are obtained for benchmark test cases from [1]-[3] with as many as 13659 buses. In all cases, the solutions obtained are not more than 0.32% worse than the best-known solutions.

Keywords:Optimization, Optimization algorithms, Computational methods Abstract: Some of the strongest polynomial-time relaxations to NP-hard combinatorial optimization problems are semidefinite programs (SDPs), but their solution complexity of up to O(n^{6.5}L) time and O(n^{4}) memory for L accurate digits limits their use in all but the smallest problems. Given that combinatorial SDP relaxations are often sparse, a technique known as chordal conversion can sometimes reduce complexity substantially. In this paper, we describe a modification of chordal conversion that allows any general-purpose interior-point method to solve a certain class of sparse SDPs with a guaranteed complexity of O(n^{1.5}L) time and O(n) memory. To illustrate the use of this technique, we solve the MAX k-CUT relaxation and the Lovasz Theta problem on power system models with up to n=13659 nodes in 5 minutes, using SeDuMi v1.32 on a 1.7 GHz CPU with 16 GB of RAM. The empirical time complexity for attaining L decimal digits of accuracy is approx0.001n^{1.1}L seconds.

Keywords:Optimization, Energy systems, Power generation Abstract: In a one-day ahead energy market scenario, power plant owners have to provide a power generation profile in advance. This power generation problem is addressed in this paper where a new scheduling strategy for concentrating solar power (CSP) plants with thermal energy storage (TES) is proposed. The scheduling method is based on a mixed-integer programming formulation. The main novelty of the proposal is the inclusion of a power block protection method based on a binary-regularization term that penalizes for changes of the power block output and binary constraints that limit the number of daily power block startups. Binary variables are used to avoid penalization of the power block start-up and shutdown. An interesting question is if this protection mechanism affect the economic results of the CSP plant. An evaluation of the economical impact of reducing generation schedule variability due to energy prices and weather forecast is included. The economic study shows that the proposed scheduling method provides a good trade-off between the economic profits obtained from energy sales and the protection of the power block. The study is based on a realistic simulation of a 50 MW parabolic trough collector-based CSP with TES under the assumption of participation in the Spanish day-ahead energy market scenario.

Keywords:Optimal control, Adaptive control, Linear systems Abstract: This paper proposes a memory-efficient approximate/adaptive optimal control (AOC) design of completely unknown continuous-time (CT) linear time invariant (LTI) systems, without requiring the restrictive persistence of excitation (PE) condition for parameter convergence. The AOC algorithm utilizes two layers of filtering - the first layer filters strategically eliminate the need for state derivative information, while the second layer filters provide suitable algebraic relations for iteratively obtaining the optimal policy under a milder online-verifiable initial excitation (IE) assumption. Unlike past literature, the proposed method does not require memory intensive delayed-window integrals, intelligent data-storage and restrictive PE assumption. The intermediate policies are proved to be stabilizing and converging to the optimal policy. Simulation results validate the efficacy of the proposed adaptive/approximate linear quadratic regulator (LQR) algorithm.

Keywords:Optimal control, Variational methods, Optimization Abstract: A new method is developed for solving optimal control problems whose solutions contain a nonsmooth optimal control. The method developed in this paper employs a modified form of the Legendre-Gauss-Radau (LGR) orthogonal direct collocation method in which an additional variable and two additional constraints are included at the end of a mesh interval. The additional variable is the switch time where a discontinuity occurs. The two additional constraints are a collocation condition on each differential equation that is a function of control along with a control constraint at the endpoint of the mesh interval that defines the location of the nonsmoothness. These additional constraints modify the search space of the NLP in a manner such that an accurate approximation to the location of the nonsmoothness is obtained. An example with a nonsmooth solution is used throughout the paper to illustrate the improvement of the method over the standard Legendre-Gauss-Radau collocation method.

Keywords:Optimal control, Variational methods, Optimization Abstract: A modified Legendre-Gauss-Radau collocation method is developed for solving optimal control problems whose solutions contain a nonsmooth optimal control. The method includes an additional variable that defines the location of nonsmoothness. In addition, collocation constraints are added at the end of a mesh interval that defines the location of nonsmoothness in the solution on each differential equation that is a function of control along with a control constraint at the endpoint of this same mesh interval. The transformed adjoint system for the modified Legendre-Gauss-Radau collocation method along with a relationship between the Lagrange multipliers of the nonlinear programming problem and a discrete approximation of the costate of the optimal control problem is then derived. Finally, it is shown via example that the new method provides an accurate approximation of the costate.

Keywords:Optimal control, Control applications, Switched systems Abstract: We present a control allocation framework to improve the performance of an industrial translational transport and positioning system, based on an inverted permanentmagnet linear synchronous motor. Compared to the state-of-practice control solution, the proposed allocation technique achieves enhanced tracking, improved motion freedom, and relaxed hardware design specifications.

Keywords:Optimal control Abstract: In this paper, we consider the problem of computing parameters of a discrete-time infinite-horizon optimal control objective function from (possibly finite-length) state and control sequences. To solve this problem, we propose a novel method of inverse optimal control by exploiting a recently established infinite-horizon discrete-time minimum principle. Our proposed method admits a computationally efficient online implementation in which pairs of states and controls from the state and control sequences are processed sequentially without being stored or processed as a batch. We establish conditions guaranteeing the uniqueness of the cost-function parameters computed by our proposed method and illustrate its application in simulation.

Keywords:Optimal control, Linear systems Abstract: In this paper, we consider the maximization of a quantitative metric of controllability with a constraint of L0 norm of the control input. Since the optimization problem contains a combinatorial structure, we introduce a convex relaxation problem for the sake of reducing computation burden. We prove the existence of solutions to the main problem and also give a simple condition under which the relaxed problem gives a solution to the main problem. It should be emphasized that the main problem can formulate time-varying control node selection, which attempts to extract when and where exogenous inputs should be provided in order to achieve high controllability of multi-agent systems.

Keywords:Agents-based systems, Large-scale systems, Optimal control Abstract: In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We characterize the minimal time for a discrete crowd model, both for exact and approximate controllability. This leads to an algorithm that computes the control and the minimal time. We finally present a numerical simulation.

Keywords:Agents-based systems, Reduced order modeling, Large-scale systems Abstract: In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the occupation measure of the group of agents by their moments and show how the dynamics of the moments can be modeled. Then approximate trajectories of the moments can be computed and an inverse problem is solved to recover macro-scale properties of the group of agents. To illustrate the theory, a numerical example with interactions between the agents is given.

Keywords:Agents-based systems, Optimization algorithms, Network analysis and control Abstract: We consider the problem of solving structured convex optimization problems over a network of agents with communication delays. It is assumed that each agent performs its local updates using possibly outdated information from its neighbors under the assumption that the delay with respect to each neighbor is bounded but otherwise arbitrary. The private objective of each agent is represented by the sum of two possibly nonsmooth functions one of which is composed with a linear mapping. The global optimization problem consists of the aggregate of the local cost functions and a common Lipschitz-differentiable function. In the case when the coupling between agents is represented only through the common function, we employ the primal-dual algorithm proposed by Vu and Condat. In the case when the linear maps introduce additional coupling between agents a new algorithm is developed. In both cases convergence is obtained under a strong convexity assumption. To the best of our knowledge, this is the first time that this form of delay is analyzed for a primal-dual algorithm in a message-passing local-memory model.

Keywords:Agents-based systems, Network analysis and control, Networked control systems Abstract: This paper considers a discrete-time opinion dynamics model in which each individual’s susceptibility to being influenced by others is dependent on her current opinion. We first propose a general opinion dynamics model based on the DeGroot model, with a general function to describe the functional dependence of each individual’s susceptibility to her own opinion, and characterize the set of all equilibria and stability of nontrivial equilibria. We then consider two classes of functions in which the individual’s susceptibility depends on the polarity of her opinion (i.e., how extreme her opinion is), and provide motivating social examples. First, we consider stubborn positives, who have reduced susceptibility if their opinions are at one end of the interval and increased susceptibility if their opinions are at the opposite end. Second, we consider stubborn extremists, who are less susceptible when they hold opinions at either end of the opinion interval. For each susceptibility model, we establish limiting behavior for different initial conditions. Networks consisting of individuals with both types of susceptibility functions are also considered.

Keywords:Agents-based systems, Distributed control Abstract: This paper investigates the stability of distance-based textit{flexible} undirected formations in the plane. Without rigidity, there exists a set of connected shapes for given distance constraints, which is called the ambit. We show that a flexible formation can lose its flexibility, or equivalently may reduce the degrees of freedom of its ambit, if a small disturbance is introduced in the range sensor of the agents. The stability of the disturbed equilibrium can be characterized by analyzing the eigenvalues of the linearized augmented error system. Unlike infinitesimally rigid formations, the disturbed desired equilibrium can be turned unstable regardless of how small the disturbance is. We finally present two examples of how to exploit these disturbances as design parameters. The first example shows how to combine rigid and flexible formations such that some of the agents can move freely in the desired and locally stable ambit. The second example shows how to achieve a specific shape with fewer edges than the necessary for the standard controller in rigid formations.

Keywords:Autonomous robots, Agents-based systems, Cooperative control Abstract: We consider a scenario consisting of a set of heterogeneous mobile agents located at a depot, and a set of tasks dispersed over a geographic area. The agents are partitioned into different types. The tasks are partitioned into specialized tasks that can only be done by agents of a certain type, and generic tasks that can be done by any agent. The distances between every pair of tasks are specified, and satisfy the triangle inequality. Given this scenario, we address the problem of allocating these tasks among the available agents (subject to type compatibility constraints) while minimizing the maximum cost to tour the allocation by any agent and return to the depot. This problem is NP-hard, and we give a three phase algorithm to solve this problem that provides 5-factor approximation, regardless of the total number of agents and the number of agents of each type. We also show that in the special case where there is only one agent of each type, the algorithm has an approximation factor of 4.

Keywords:Sensor networks, Optimization, Decentralized control Abstract: In many emerging applications, multiple sensors transmit their measurements to a remote estimator over a shared medium. In such a system, the optimal sampling rates at each sensor depend on the nature of the stochastic process being observed at each sensor as well as the available communication capacity. Our main contribution is to show that the problem of determining optimal sampling rates may be posed as a network utility maximization problem and solved using appropriate modifications of the standard dual decomposition algorithms for network utility maximization. We present two such algorithms, one synchronous and one asynchronous, and show that under mild technical conditions, both algorithms converge to the optimal rate allocation. We present a detailed simulation study to illustrate that the asynchronous algorithm is able to adapt the sampling rate to change in the number of sensors and the available channel capacity and is robust to packet drops.

Keywords:Networked control systems, Decentralized control, Stochastic optimal control Abstract: We consider a network of several independent linear systems controlled over a shared communication network. Data transmissions pertaining to each control loop are arbitrated by a scheduler collocated with the plant's sensors that transmits the state information to the corresponding remote controller collocated with the plant's actuators. The shared communication channel is assumed to be operating based on a contention-based protocol, endowing the networked control system with desirable reconfigurable and scalable features. We propose a class of scheduling policies which admit a decentralized optimal control implementation and an event-triggered policy within this class which is shown to be consistent, i.e. it results in a better control performance for any linear system, measured by an average quadratic cost than its non-event-based counterpart.

Keywords:Networked control systems, Control over communications, Optimal control Abstract: In this work we address the problem of LQG control where the communication between the sensor and the controller/actuator is performed via Wi-Fi. We exploit one feature of Wi-Fi (standard IEEE 802.11) which gives the ability to switch among different data-rates in real-time: a lower transmission rate provides a lower packet loss probability at a price of a larger sampling period. As a matter of fact, it is not obvious how to select the optimal rate from a control perspective. Nevertheless, the packet error probability as a function of the perceived SNR can be obtained either analytically or empirically. Based on these curves, we determine the optimal rate and the optimal LQG controller for any fixed SNR. In a scenario with a time-varying SNR, we also propose a rate adaptation strategy which is triggered by the measured SNR. Numerical simulations and comparisons with current literature are included to show the benefits of our approach.

Keywords:Queueing systems, Delay systems, Discrete event systems Abstract: In the design of shared resource networked control systems (NCSs), resource managers play an important role to appropriately allocate limited resources across the distributed system. They are often used to fairly distribute the limited bandwidth among the medium-sharing entities at the expense of delaying or discarding unnecessary data samples. Considering the rapidly growing volume of information being exchanged, a relevant scenario for efficient resource management is state-dependent data buffering via network queues. In this paper, we propose state-dependent data buffering for shared-resource NCSs, such that the buffer state, i.e. queue length, can be controlled depending on the real-time conditions of both the control systems and the communication network. We consider that the transmission decisions at the sensor sides are taken by event-based schedulers, and those data eventually sent for transmission are queued and processed depending on the available communication resource. We derive sufficient conditions under which the NCS with the proposed cross-layer transmission scheme is stable in almost sure mean-square sense. Moreover, we show performance improvements resulting from our proposed design in comparison with its state-independent counterpart.

Keywords:Networked control systems, Control over communications, Communication networks Abstract: The flexibility of a control system can be improved by closing the loop over a wireless network. In these systems, however, the controller is generally assigned to the plant a priori. In this paper, a novel distributed control architecture called the broadcast control system is introduced. In this system the plant broadcasts its state to multiple controllers, where each controller makes a local decision to send back the control input. This allows the plant to use different controllers while moving. Moreover, the control performance can be optimized by exploiting the diversity of the wireless links. A contention resolution phase is introduced, which dynamically assigns a controller to the plant at runtime based on the wireless link quality. The coordinate descent algorithm is proposed as an effective way to optimize the thresholds of the contention resolution phase. The subproblem structure of the objective function is used to prove the convergence of the optimization algorithm. Numerical results show that the control performance can be increased by adding more controllers to the system, which is particularly effective when the link quality is poor.

Keywords:Delay systems, Control over communications, Stochastic optimal control Abstract: In the design of closed-loop networked control systems (NCSs), induced transmission delay between sensors and the control station is an often-present issue which compromises control performance and may even cause instability. A very relevant scenario in which network-induced delay needs to be investigated is costly usage of communication resources. More precisely, advanced communication technologies, e.g. 5G, are capable of offering latency-varying information exchange for different prices. Therefore, induced delay becomes a decision variable. It is then the matter of decision maker's willingness to either pay the required cost to have low-latency access to the communication resource, or delay the access at a reduced price. In this article, we consider optimal price-based bi-variable decision making problem for single-loop NCS with a stochastic linear time-invariant system. Assuming that communication incurs cost such that transmission with shorter delay is more costly, a decision maker determines the switching strategy between communication links of different delays such that an optimal balance between the control performance and the communication cost is maintained. In this article, we show that, under mild assumptions on the available information for decision makers, the separation property holds between the optimal link selecting and control policies. As the cost function is decomposable, the optimal policies are efficiently computed.

Keywords:Optimization algorithms, Randomized algorithms, Agents-based systems Abstract: We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gra- dient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses Hessian information to accelerate convergence. We analyze our method under the general asynchronous model of computation, in which each function is selected infinitely often with possibly unbounded (but sublinear) delay. For strongly convex problems, we establish linear convergence for the SUCAG method. When the initialization point is sufficiently close to the optimal solution, the established convergence rate is only dependent on the condition number of the problem, making it strictly faster than the known rate for the SAGA method. Furthermore, we describe a Markov-driven approach of implementing the SUCAG method in a distributed asynchronous multi-agent setting, via gossiping along a random walk on an undirected communication graph. We show that our analysis applies as long as the graph is connected and, notably, estab- lishes an asymptotic linear convergence rate that is robust to the graph topology. Numerical results demonstrate the merits of our algorithm over existing methods.

Keywords:Optimization algorithms, Optimization Abstract: In this paper, we develop a class of distributed Fenchel dual gradient methods that enable a smoothing technique in order to solve nonsmooth convex optimization over networks with time-varying topologies, where the nodes are required to find a global optimal decision that minimizes the sum of their own objectives subject to their individual constraints. Specifically, we first apply a smoothing technique to the Fenchel dual of the problem, so that a strongly convex and smooth approximation of the Fenchel dual function can be obtained. We then adopt a family of weighted gradient methods to solve such a smoothed Fenchel dual problem, which can be implemented over time-varying networks in a decentralized fashion. Under a standard network connectivity condition, we derive a linear rate of convergence to the optimal value of the smoothed Fenchel dual problem for the proposed algorithms. Based on this result, we further show that an approximate primal solution reaches epsilon-accuracy in optimality and feasibility of the original problem within O((1/epsilon^2)*ln(1/epsilon)) iterations.

Keywords:Optimization algorithms, Distributed control Abstract: In this paper, we propose a distributed algorithm to solve multi-agent constrained optimization problems. Specifically, we employ the recently developed Accelerated Distributed Augmented Lagrangian (ADAL) algorithm that has been shown to exhibit faster convergence rates in practice compared to relevant distributed methods. Distributed implementation of ADAL depends on separability of the global coupling constraints. Here we extend ADAL so that it can be implemented distributedly independent of the structure of the coupling constraints. For this, we introduce local estimates of the global constraint functions and multipliers and employ a finite number of consensus steps between iterations of the algorithm to achieve agreement on these estimates. The proposed algorithm can be applied to both undirected or directed networks. Theoretical analysis shows that the algorithm converges at rate O(1/k) and has steady error that is controllable by the number of consensus steps. Our numerical simulation shows that it outperforms existing methods in practice.

Keywords:Optimization, Distributed control, Machine learning Abstract: The problem of finding the minimizer of a sum of convex functions is central to the field of distributed optimization. Thus, it is of interest to understand how that minimizer is related to the properties of the individual functions in the sum. In this paper, we provide an upper bound on the region containing the minimizer of the sum of two strongly convex functions. We consider two scenarios with different constraints on the upper bound of the gradients of the functions. In the first scenario, the gradient constraint is imposed on the location of the potential minimizer, while in the second scenario, the gradient constraint is imposed on a given convex set in which the minimizers of two original functions are embedded. We characterize the boundaries of the regions containing the minimizer in both scenarios.

Keywords:Optimization algorithms Abstract: We consider a distributed optimization problem over a network of agents aiming to minimize a global objective function that is the sum of local convex and composite cost functions. To this end, we propose a distributed Chebyshev-accelerated primal-dual algorithm to achieve faster ergodic convergence rates. In standard distributed primal-dual algorithms, the speed of convergence towards a global optimum (i.e., a saddle point in the corresponding Lagrangian function) is directly influenced by the eigenvalues of the Laplacian matrix representing the communication graph. In this paper, we use Chebyshev matrix polynomials to generate gossip matrices whose spectral properties result in faster convergence speeds, while allowing for a fully distributed implementation. As a result, the proposed algorithm requires fewer gradient updates at the cost of additional rounds of communications between agents. We illustrate the performance of the proposed algorithm in a distributed signal recovery problem. Our simulations show how the use of Chebyshev matrix polynomials can be used to improve the convergence speed of a primal-dual algorithm over communication networks, especially in networks with poor spectral properties, by trading local computation by communication rounds.

Keywords:Optimization, Optimization algorithms Abstract: Continuous time primal-dual gradient dynamics that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and control. While the global asymptotic stability of such dynamics has been well-studied, it is less studied whether they are globally exponentially stable. In this paper, we study the primal-dual gradient dynamics for convex optimization with strongly-convex and smooth objectives and affine equality or inequality constraints, and prove global exponential stability for such dynamics. Bounds on decaying rates are provided.

Keywords:Transportation networks, Network analysis and control, Traffic control Abstract: It is known that autonomous vehicles are capable of maintaining shorter headways and distances when they form platoons of vehicles. Thus, deployment of autonomous vehicles can result in roadway flow capacity increases in traffic networks. Consequently, it is envisioned that their deployment will boost the overall capacity of the network. In this paper, we consider a nonatomic routing game on a traffic network with inelastic (fixed) demands for the set of network O/D pairs, and study how replacing a fraction of regular (i.e. nonautonomous) vehicles by autonomous vehicles will affect the network total delay, under the assumption that the vehicles choose their routes selfishly. Using well known US bureau of public roads (BPR) traffic delay models, we show that the resulting Wardrop equilibrium is not necessarily unique even in its weak sense for networks with mixed autonomy. We derive the conditions under which the total network delay is guaranteed to not increase as a result of increasing the ratio of autonomous vehicles. However, we also show that when these conditions do not hold, counter intuitive behaviors might occur: the total delay can grow by increasing the fraction of autonomous vehicles in the network. In particular, we prove that for networks with a single O/D pair, if the road degree of capacity asymmetry (i.e. the ratio between the road capacity when all vehicles are regular and the road capacity when all vehicles are autonomous) is homogeneous, the total network delay is 1) unique, and 2) a nonincreasing continuous function of network autonomy fraction. We show that for heterogeneous degrees of capacity asymmetry, the total delay is not unique, and it can further grow when the fraction of autonomous vehicles increases. We demonstrate that similar behaviors may be observed in networks with multiple O/D pairs.

Keywords:Transportation networks, Stochastic systems, Network analysis and control Abstract: Vehicle sharing system consists of a fleet of vehicles (usually bikes or cars) that can be rented at one station and returned at another station. We study how to achieve guaranteed service availability in such systems. Specifically, we are interested in determining a)~the fleet size and initial allocation of vehicles to stations and b)~the minimum capacity of each station needed to guarantee that a)~every customer will find an available vehicle at the origin station and b)~the customer will find a free parking spot at the destination station. We model the evolution of number of vehicles at each station as a stochastic process and prove that the relevant probabilities in the system can be approximated from above using a computationally-tractable decoupled model. This propertycan be exploited to determine the size of fleet and initial distribution of vehicles that are sufficient to achieve the desired service level. The applicability of the method is demonstrated by computing the fleet size, initial distribution of vehicles, and capacities of stations that would be needed to avoid vehicle shortage events in Boston's bike sharing system "The Hubway". Our simulation shows that the proposed method allocates available vehicles to stations more efficiently than the naive approach and thus it is able to achieve the equivalent quality of service level with half of the vehicle fleet and half of the parking capacity.

Keywords:Transportation networks, Autonomous vehicles, Traffic control Abstract: The emerging technology enabling autonomy in vehicles has led to a variety of new problems in transportation networks, such as planning and perception for autonomous vehicles. Other works consider social objectives such as decreasing fuel consumption and travel time by platooning. However, these strategies are limited by the actions of the surrounding human drivers. In this paper, we consider proactively achieving these social objectives by influencing human behavior through planned interactions. Our key insight is that we can use these social objectives to design local interactions that influence human behavior to achieve these goals. To this end, we characterize the increase in road capacity afforded by platooning, as well as the vehicle configuration that maximizes road capacity. We present a novel algorithm that uses a low-level control framework to leverage local interactions to optimally rearrange vehicles. We showcase our algorithm using a simulated road shared between autonomous and human-driven vehicles, in which we illustrate the reordering in action.

Keywords:Autonomous vehicles, Traffic control, Transportation networks Abstract: In this paper, we adobe the Stochastic Fluid Modeling framework to model the critical density of a road network and we employ the routereservation scheme (as proposed in [1], [2]) to control traffic for a congestion-free operation. To derive the network’s critical density value, we employ Infinitesimal Perturbation Analysis (IPA) that provides a stochastic approximation which can be utilized in an on-line fashion to capture the dynamic changes in the critical density value as a consequence of different incidents.

Keywords:Modeling, Transportation networks Abstract: With the focus set on water distribution networks, dynamics typically play a subordinate role in the modeling procedure. This paper intends to draw a different picture, where flow dynamics would allow engineers to gain more physical insight while offering them more sophisticated tools for manipulation. The handling of consumption values is crucial in this regard as it is the major drive for the flow distribution in the network’s topology. Simulations with the derived model, incorporating linear consumption dynamics, are compared with measurements on a real experimental network. Moreover, the equivalence of the model’s equilibrium with the conventional steady-state equations is proven.

Keywords:Optimization, Optimization algorithms, Transportation networks Abstract: We examine the effect of malicious attacks in disrupting optimal routing algorithms for transportation networks. We model traffic networks using the cell transmission model, which is a spatiotemporal discretization of kinematic wave equations. Here, vehicles are modeled as masses and roads as cells, and traffic flow is subject to conservation of mass and capacity constraints. At time zero a resource-constrained malicious agent reduces the capacities of cells so as to maximize the amount of time mass spends in the network. For the resulting set of capacities the network router then solves a linear program to determine the flow configuration that minimizes the amount of time mass spends in the network. Our model allows for the outright or partial failure of road cells at time zero, the effects of which can cause cascading failure in the network due to irreversible blockages resulting from congestion. This two-player problem is written as a max-min optimization and is reformulated to an equivalent nonconvex optimization problem with a bilinear objective and linear constraints. Linearization techniques are applied to the optimization problem to find local solutions. Analyzing illustrative examples shows that attackers with relatively small resource budgets can cause widespread failure in a traffic network.

Keywords:Constrained control, Optimization algorithms, Numerical algorithms Abstract: In this paper, we develop an architecture for accelerating a primal-dual quadratic program solver associated with linear model predictive control on a Field Programmable Gate Array (FPGA). The architecture exploits the saddle-point structure of the quadratic program and allows for transparent introduction of pre-conditioning and relaxation to improve solution robustness and convergence. We demonstrate the efficiency of the architecture using fixed-point arithmetic implementation and taking advantage of the sparsity of the problem data to increase scalability and solution speed.

Keywords:Constrained control, Lyapunov methods, Algebraic/geometric methods Abstract: This paper focuses on the attitude constrained control of a rigid body in three dimensions, and proposes the Explicit Reference Governor (ERG) as a solution to handle constraints on SO(3). Two types of constraints are considered: (i) input torque constraints, and (ii) geometric conic pointing constraints. The objective of this paper is to design a control law that is able to steer the attitude of the rigid body to the desired attitude reference while enforcing constraints satisfaction at all times. To do so, the first step is to design a controller that makes the desired attitude asymptotically stable when constraints (i) and (ii) are neglected. Then, the proposed control scheme is augmented with a suitably designed ERG to add constraint-handling capabilities to the scheme. All the proposed solutions are defined in terms of elements on SO(3) and do not make use of any parameterizations as e.g., quaternions and Euler angles. Finally, numerical simulations are carried out to show the effectiveness of the proposed control scheme.

Keywords:Constrained control, Predictive control for linear systems, Optimization Abstract: This paper presents a computationally efficient solution for constraint management of square multi-input and multi-output (MIMO) systems. The solution, referred to as the Decoupled Reference Governor (DRG), maintains the highly-attractive computational features of Scalar Reference Governors (SRG) while having performance comparable to Vector Reference Governors (VRG). DRG is based on decoupling the input-output dynamics of the system, followed by the deployment of a bank of SRGs for each decoupled channel. We present a detailed set-theoretic analysis of DRG, which highlights its main characteristics. A quantitative comparison between DRG and the VRG is also presented in order to illustrate the computational advantages of DRG.

Keywords:Constrained control, Lyapunov methods, Optimization Abstract: We study the problem of using imperfect state feedback to stabilize polynomial, control-affine systems which are subject to polytopic input constraints. The state feedback is assumed be subject to an additive, unknown, but bounded disturbance. An analysis framework based on Sum-of-Squares (SOS) programming is developed, in order to characterize the subset of the measurement space from where stabilization to a neighborhood of the origin with a Lyapunov-based, input constrained control law is guaranteed for the particular measurement assumptions. Subsequently, such a control law is developed based on the minimizer, at every (measured) state, of a low-dimension Quadratic Program (QP). The proposed control solution is designed in a way such that attempting to render the system stable from the perspective of a control law with knowledge of the imperfect measurement of the state implies the stabilization of the actual system. The stabilization guarantees provided by the SOS analysis part, combined with the efficiency of the QP-based control law make the proposed solution suitable for systems where embeddability, robustness to measurement disturbances and safety are important. Numerical simulations are used to illustrate the main contributions.

Keywords:Constrained control, Optimal control, Predictive control for linear systems Abstract: We investigate strict dissipativity and turnpike properties for indefinite discrete-time linear quadratic optimal control problems in the presence of constraints on state and input. Previous results provide a geometric characterization of these properties in case that the stage cost is convex. We generalize these results to indefinite cost functions using two approaches: First, we show that the existing framework can be extended to indefinite state weighting if the stage cost accumulated over multiple consecutive time steps is convex. As a second contribution, we study the strict dissipation inequality by taking the particular shape of the constraints into account. This allows us to state sufficient conditions for strict dissipativity and turnpike properties where the occurrence of turnpikes on the boundary of the constraints is directly related to negative eigenvalues of the cost.

Keywords:Constrained control, Optimization algorithms, Control system architecture Abstract: Recent advances in embedded model predictive control (MPC) have paved the way for MPC technology in high-speed systems and resource-constrained applications. In this paper, we exploit analog circuit emulation of constrained Linear Quadratic (LQ) problem for rapid prototyping of MPC on fast reconfigurable analog processors such as Field Programmable Analog Arrays (FPAA). The inherent massively parallel structure of the underling solution dynamics and the possibility of signal scaling through appropriate pre-conditioning mean that MPC can be reliably implemented using low-power ultra-fast analog circuits. The effectiveness of the approach is demonstrated for a two-integrator MPC problem.

Keywords:Genetic regulatory systems, Systems biology, Nonlinear systems identification Abstract: Sharing of cellular resources in genetic circuits negatively affects performance and often leads to unpredictable behavior. Measuring key metrics from experimental data that quantify resource sharing and its effect on a system's output would be highly useful. In this paper, we propose two metrics, Q and S, representing the quantity of resources used by a genetic circuit module and the sensitivity of the output of a module to resource disturbances, respectively. Together, Q and S may be used to estimate the change in the output of a module in response to the disturbances in the availability of resources. We cast the problem of finding these metrics as a parameter estimation problem and outline a simple procedure to estimate these metrics from data. Knowledge of Q and S for a circuit module enables prediction of the effects of resource sharing and allows for resource-aware design of genetic circuits.

Keywords:Biomolecular systems, Cellular dynamics, Identification Abstract: The fact that genes compete for shared cellular resources poses a fundamental challenge when identifying parameters of genetic parts. A recently developed model of gene expression tackles this problem by explicitly accounting for resource competition. In addition to accurately describing experimental data, this model only depends on a small number of easily identifiable parameters with clear physical interpretation. Based on this model, we outline a procedure to select the optimal set of experiments to characterize biomolecular parts in synthetic biology. Additionally, we reveal the role competition for shared resources plays, provide guidelines how to minimize its detrimental effects, and how to leverage this phenomenon to extract the most information about unknown parameters. To illustrate the results, we consider the case of part characterization in cell-free extracts, treat plasmid DNA concentrations as decision variables, and demonstrate the significant performance difference between naive and optimal experiment design.

Keywords:Nonlinear systems identification, Biomolecular systems, Modeling Abstract: Synthetic biology is an emerging engineering discipline that aims at synthesising logical circuits into cells to accomplish new functions. Despite a thriving community and some notable successes, the basic task of assembling predictable gene circuits is still a key challenge. Mathematical models are uniquely suited to help solve this issue. Yet in biology they are perceived as expensive and laborious to obtain because low-information experiments have often been used to infer model parameters. How much additional information can be gained using optimally designed experiments? To tackle this question we consider a building block in Synthetic Biology, an inducible promoter in yeast S. cerevisiae. Using in vivo data we re-fit a mathematical model for such a system; we then compare in silico the quality of the parameter estimates when model calibration is done using typical (e.g. step inputs) and optimally designed experiments. We find that Optimal Experimental Design leads to ~70% improvement in the predictive ability of the inferred models. We conclude providing suggestions on how optimally designed experiments can be implemented in vivo.

Keywords:Biomolecular systems, Markov processes, Genetic regulatory systems Abstract: A central issue in the analysis of multi-stable systems is that of controlling the relative size of the basins of attraction of alternative states through suitable choices of system parameters. We are interested here mainly in the stochastic version of this problem, that of shaping the stationary probability distribution of a Markov chain so that various alternative modes become more likely than others.

Although many of our results are more general, we were motivated by an important biological question, that of cell differentiation. In the mathematical modeling of cell differentiation, it is common to think of internal states of cells (quanfitied by activation levels of certain genes) as determining the different cell types. Specifically, we study here the ``PU.1/GATA-1 circuit'' which is involved in the control of the development of mature blood cells from hematopoietic stem cells (HSCs). All mature, specialized blood cells have been shown to be derived from multipotent HSCs.

Our first contribution is to introduce a rigorous chemical reaction network model of the PU.1/GATA-1 circuit, which incorporates current biological knowledge. We then find that the resulting ODE model of these biomolecular reactions is incapable of exhibiting multistability, contradicting the fact that differentiation networks have, by definition, alternative stable steady states. When considering instead the stochastic version of this chemical network, we analytically construct the stationary distribution, and are able to show that this distribution is indeed capable of admitting a multiplicity of modes. Finally, we study how a judicious choice of system parameters serves to bias the probabilities towards different stationary states. We remark that certain changes in system parameters can be physically implemented by a biological feedback mechanism; tuning this feedback gives extra degrees of freedom that allow one to assign higher likelihood to some cell types over others.

Keywords:Biological systems, Systems biology, Stochastic systems Abstract: Given a stochastic biomolecular chemical reaction network, a reference input and a designated molecular species to be regulated, the antithetic integral feedback molecular motif introduced in [Briat, Gupta & Khammash, Cell Systems, 2016] was shown to guarantee network ergodicity, robust disturbance rejection, and a zero steady-state tracking error (robust perfect adaptation). While these favorable properties are guaranteed for the mean dynamics, the controlled network may in fact have an increased output variance due to the inevitable molecular noise introduced by the controller. In this paper we show that, in the context of gene expression, the stationary protein variance can be decreased and the system performance improved by combining the antithetic integral feedback motif with a negative feedback control strategy. It is demonstrated the smaller the variance of the proteins, the larger the settling-time of its mean trajectory, which underscores a basic trade-off between these two objectives.

Keywords:Genetic regulatory systems, Systems biology, Output regulation Abstract: In this letter, we analyze a genetic toggle switch recently studied in the literature where the expression of two repressor proteins can be tuned by controlling two different inputs, namely the concentration of two inducer molecules in the growth medium of the cells. Specifically, we investigate the dynamics of this system when subject to pulse-width modulated (PWM) inputs. We provide an analytical model that captures qualitatively the experimental observations reported in the literature and approximates its asymptotic behavior. We also discuss the effect that the system parameters have on the prediction accuracy of the model. Moreover, we propose a possible external control strategy to regulate the mean value of the fluorescence of the reporter proteins when the cells are subject to such periodic forcing.

Keywords:Game theory, Control applications Abstract: We study a dynamical model of a population of cooperators and defectors whose actions have long-term consequences on environmental "commons" - what we term the "resource". Cooperators contribute to restoring the resource whereas defectors degrade it. The population dynamics evolve according to a replicator equation coupled with an environmental state. Our goal is to identify methods of influencing the population with the objective of maximizing accumulation of the resource. In particular, we consider strategies that modify individual-level incentives. We then extend the model to include a public opinion state that imperfectly tracks the true environmental state, and study strategies that influence opinion. We formulate optimal control problems and solve them using numerical techniques to characterize locally optimal control policies for three problem formulations: 1) control of incentives, and control of opinions through 2) propaganda-like strategies and 3) awareness campaigns. We show numerically that the resulting controllers in all formulations achieve the objective, albeit with an unintended consequence. The resulting dynamics include cycles between low and high resource states - a regime termed an "oscillating tragedy of the commons". This outcome may have desirable average properties, but includes risks to resource depletion. Our findings suggest the need for new approaches to controlling population-environment dynamics.

Keywords:Game theory, Optimization, Agents-based systems Abstract: Consider a multiplayer game, and assume a system level objective function, which the system wants to optimize, is given. This paper aims at accomplishing this goal via potential game theory when players can only get part of other players' information. The technique is to design local information based utility functions, so that designed game is a potential game with the system level objective function as its potential function. First, the existence of local information based utility functions can be verified by checking whether the corresponding linear equations have a solution. Then an algorithm is proposed to calculate the local information based utility functions when the utility design equations have solutions. Finally, consensus problem of multiagent system is considered to demonstrate the effectiveness of the proposed design procedure.

Keywords:Game theory, Energy systems, Smart grid Abstract: The problem of designing revenue optimal mechanisms for allocation of a number of goods to consumers during T time steps is considered. Each consumer wants to receive E units of the good and has a delivery rate constraint that limits the number of goods it can receive within one time step. Each consumer’s rate constraint and valuation for the goods are its private information. Resource allocation problems of this type commonly arise in the context of energy services where consumers have a tolerable rate of energy delivery that cannot be exceeded when they receive their demanded energy. We characterize the allocation rule for a Bayesian incentive compatible, individually rational and revenue maximizing mechanism in terms of solutions to integer programs. The corresponding payment rule is also pinned down by the allocation rule in the form of an integral equation. We then reformulate the problem of finding the optimal allocations as a network flow optimization problem. A complete characterization of the optimal allocations and payments is then provided in terms of the solution to the corresponding network flow optimization problem which can be obtained efficiently using the methods developed in the context of discrete optimization [1], [2]. A numerical example is provided to verify our results.

Keywords:Game theory, Networked control systems, Distributed control Abstract: How does system-level information impact the ability of an adversary to degrade performance in a networked control system? In this work, we focus on this question in the context of graphical coordination games where an adversary can influence a given fraction of the agents in the system. Focusing on the class of ring graphs, we explicitly highlight how knowledge of the graph structure and agent identities can be exploited by an adversary to significantly degrade system performance. Further, we demonstrate how the lack of such knowledge drastically reduces the potential harm an adversary can do to the system.

Keywords:Game theory, Communication networks, Linear systems Abstract: The main objective of this paper consists in providing definitions and preliminary results that allow to assess and evaluate the importance of information and data exchange patterns in non-cooperative dynamic games defined over (communication or physical) networks. This objective is achieved by introducing suitable metrics that associate a value to each communication link among the agents. In the case of Linear-Quadratic (LQ) games on networks, necessary and sufficient conditions are then provided that allow to characterize the set of all Nash equilibria that can be generated for a given network topology, namely even in the presence of partial and limited information.

Keywords:Markov processes, Game theory, Stochastic optimal control Abstract: In this paper, the static output feedback (SOF) Stackelberg strategy for continuous-time Markov jump linear stochastic systems (MJLSSs) governed by an Ito differential equation with H-infinity constraints involving multiple decision makers is investigated for the first time. First, the linear quadratic regulator (LQR) problem is discussed in terms of the SOF. It is shown that the required solutions can be computed by solving the cross-coupled stochastic algebraic Lyapunov type equations (CCSLTEs). Although the proposed approach is based on the classical Lagrange-multipliers technique, treatment of the bilinear matrix inequalities (BMIs) can be avoided. Second, the SOF strategy is also shown to be obtained by solving the CCSALTEs for the follower's strategies set. As another important contribution of this paper, a numerical algorithm based on an improved fixed point iterations is proposed to reduce computational burden and to guarantee the convergence. Finally, to demonstrate the existence and effectiveness of the proposed SOF Stackelberg strategy set, a simple academic example is demonstrated.

Keywords:Learning, Uncertain systems, Autonomous robots Abstract: Standard methods for synthesis of control policies in Markov decision processes with unknown transition probabilities largely rely on a combination of exploration and exploitation. While these methods often offer theoretical guarantees on system performance, the number of time steps and samples needed to initially explore the environment before synthesizing a well-performing control policy is impractically large. This paper partially alleviates such a burden by incorporating a priori existing knowledge into learning, when such knowledge is available. Based on prior information about bounds on the differences between the transition probabilities at different states, we propose a learning approach where the transition probabilities at a given state are not only learned from outcomes of repeatedly performing a certain action at that state, but also from outcomes of performing actions at states that are known to have similar transition probabilities. Since the directly obtained information is more reliable at determining transition probabilities than second-hand information, i.e., information obtained from similar but potentially slightly different states, samples obtained indirectly are weighted with respect to the known bounds on the differences of transition probabilities. While the proposed strategy can naturally lead to errors in learned transition probabilities, we show that, by proper choice of the weights, such errors can be reduced, and the number of steps needed to form a near-optimal control policy in the Bayesian sense can be significantly decreased.

Keywords:Learning, Distributed parameter systems, Sensor networks Abstract: We propose a geometric reinforcement learning algorithm for real-time path planning for mobile sensor networks (MSNs) in the problem of reconstructing a spatialtemporal varying ﬁeld described by the advection-diffusion partial differential equation. A Luenberger state estimator is provided to reconstruct the concentration ﬁeld, which uses the collected measurements from a MSN along its trajectory. Since the path of the MSN is critical in reconstructing the ﬁeld, a novel geometric reinforcement learning (GRL) algorithm is developed for the real-time path planning. The basic idea of GRL is to divide the whole area into a series of lattice to employ a speciﬁc time-varying reward matrix, which contains the information of the length of path and the mapping error. Thus, the proposed GRL can balance the performance of the ﬁeld reconstruction and the efﬁciency of the path. By updating the reward matrix, the real-time path planning problem can be converted to the shortest path problem in a weighted graph, which can be solved efﬁciently using dynamic programming. The convergence of calculating the reward matrix is theoretically proven. Simulation results serve to demonstrate the effectiveness and feasibility of the proposed GRL for a MSN.

Keywords:Learning, Mechatronics, Lyapunov methods Abstract: This paper describes a procedure to design a path following controller of port-Hamiltonian systems based on training trajectory data. In order to calculate the reasonable design parameters for path following controller from the training data, Bayesian inference is adopted in this paper. By using Bayesian inference, not only the mean value of the trajectory but also the covariance matrix is acquired. By incorporating the covariance information into the control system design, it is expected to create a potential function that takes into account uncertainty at each position on the trajectory.

Keywords:Learning, Uncertain systems, Optimization algorithms Abstract: This paper considers a class of real-time decision making problems to minimize the expected value of a function that depends on a random variable xi under an unknown distribution mathbb{P}. In this process, samples of xi are collected sequentially in real time, and the decisions are made, using the real-time data, to guarantee out-of-sample performance. We approach this problem in a distributionally robust optimization framework and propose a novel Online Data Assimilation Algorithm for this purpose. This algorithm guarantees the out-of-sample performance in high probability, and gradually improves the quality of the data-driven decisions by incorporating the streaming data. We show that the Online Data Assimilation Algorithm guarantees convergence under the streaming data, and a criteria for termination of the algorithm after certain number of data has been collected.

Keywords:Learning, Networked control systems, Markov processes Abstract: The goal of this paper is to study a distributed version of the gradient temporal-difference (GTD) learning algorithm for multi-agent Markov decision processes (MDPs). The temporal-difference (TD) learning is a reinforcement learning (RL) algorithm which learns an infinite horizon discounted cost function (or value function) for a given fixed policy without the model knowledge. In the distributed RL case each agent receives local reward through a local processing. Information exchange over sparse communication network allows the agents to learn the global value function corresponding to a global reward, which is a sum of local rewards. In this paper, the problem is converted into a constrained convex optimization problem with a consensus constraint. Then, we propose a primal-dual distributed GTD algorithm and prove that it almost surely converges to a set of stationary points of the optimization problem.

Keywords:Learning, Human-in-the-loop control, Robotics Abstract: Human operators of construction and farming equipment exhibit strong situational awareness which enables them to execute tasks while robustly handling unexpected uncertainties in the environment. Automatic control, on the other hand, is generally capable of executing repetitive and well-defined tasks more efficiently and precisely. Collaboratively achieving the tasks by combining the benefits of critical situational awareness and decision making capabilities of human operators and the efficiency and accuracy of automatic control is expected to provide improved performance of these tasks. Development of methods in learning, prediction and human-machine shared control to improve such collaborative task execution and application to hydraulic excavators is the focus of this work. In this paper, we propose a task learning method based on an operator primitives based segmentation (OPbS) and Bayesian non-parametric clustering with temporal ordering (BNPC/TO). Then, we introduce a method for predicting the operator's intent in a dynamical environment by proposing an empirical stochastic transition matrix (ESTM) and a dynamic angle difference exponential (DADE). We then provide a design for blended shared control with conflict-awareness (BSC/CA) extended from the dynamic angle difference. Finally, we evaluate the approach on a scaled hydraulic excavator test-platform for a typical earth-moving task with novice learning operators and a skilled demonstration operator.

Keywords:Robotics, Estimation, Robust control Abstract: This work deals with the problem of path tracking of a suspended load using a tilt-rotor UAV. Such task requires the knowledge of the load position, which may not be provided by available sensors. Therefore, to accomplish the path tracking, a set-valued state estimator based on constrained zonotopes is proposed to solve the problem of estimating the load position and orientation, considering sensors with different sampling times, and unknown-but-bounded disturbances. Moreover, to provide feedback to the controller based on the estimated state set, an optimal state choice is given according to a proposed constrained minimum-variance criteria. The path tracking is then solved by a discrete-time mixed H2/H-infinity controller with pole-placement constraints. Results from numerical experiments, performed in a platform based on the Gazebo simulator with a Computer Aided Design (CAD) model of the system, are presented to corroborate the performance of the set-valued state estimator along with the designed controller.

Keywords:Nonholonomic systems, Robotics, Modeling Abstract: This article studies the motion of a vertical rolling disk on an arbitrary smooth surface in Re^3. The disk can roll without slipping about its axis and turn about the surface normal. A global formulation for the dynamics of the rolling disk is proposed without the use of local coordinates, and the model is globally defined on the manifold without singularities or ambiguities. The theoretical results are specialized for two different surfaces; on a flat surface and on a spherical surface. The proposed motion planning algorithm consists of three phases and each phase is a rest-to-rest maneuver, such that the rolling disk is stationary at both the start and the end of each phase. Simulation results are included that show effectiveness of the motion planning algorithm on the smooth surfaces.

Keywords:Robotics, Autonomous systems Abstract: In this paper, a method to synthesize controllers using finite time convergence control barrier functions guided by linear temporal logic specifications for continuous time multi-agent dynamical systems is proposed. Finite time convergence to a desired set in the state space is guaranteed under the existence of a suitable finite time convergence control barrier function. In addition, these barrier functions also guarantee forward invariance once the system converges to the desired set. This allows us to formulate a theoretical framework which synthesizes controllers for the multi-agent system. These properties also enable us to solve the reachability problem in continuous time by formulating a theorem on the composition of multiple finite time convergence control barrier functions. This approach is more flexible than existing methods and also allows for a greater set of feasible control laws. Linear temporal logic is used to specify complex task specifications that need to be satisfied by the multi-agent system. With this solution methodology, a control law is synthesized that satisfies the given temporal logic task specification. Robotic experiments are provided which were performed on the Robotarium multi-robot testbed at Georgia Tech.

Keywords:Maritime control, Control applications, Robotics Abstract: This paper presents a 3D reactive collision avoidance algorithm for vehicles with underactuated dynamics. The underactuated states cannot be directly controlled, but are controlled indirectly by steering the direction of the vehicle’s velocity vector. This vector is made to point a constant avoidance angle away from the obstacle, thus ensuring collision avoidance, while the forward speed is kept constant to maintain maneuverability. We choose an optimal pair of desired heading and pitch angles during the maneuver, thus taking advantage of the flexibility provided by operating in 3D. The algorithm incorporates limits on both the allowed pitch angle and the control inputs, which are limits that often are present in practical scenarios. Finally, we provide a mathematical proof that the collision avoidance maneuver is safe, and support the analysis through several simulations.

Keywords:Robotics, Modeling, Simulation Abstract: This paper presents some preliminary results concerning a new foot placement algorithm for dynamically stable legged locomotion. For this, the nonlinear model of a particular spherical inverted pendulum is derived, using D’Alembert’s principle. A set of conditions is obtained, for the initial angles of the pendulum, such that a certain convenient trajectory of the center of mass is assured for a given initial linear velocity of the center of mass. Finally, a simple algorithm for finding an initial point is proposed.

Keywords:Robotics, Control applications, Human-in-the-loop control Abstract: This paper presents a novel control algorithm for haptic-enabled bilateral teleoperation systems involving several degrees of freedom. In particular, the contribution focuses on the implementation of a passivity layer for an established time domain scheme. The proposed approach aims at preserving transparency of interaction along subsets of the environment space which are preponderant for the given task, while guaranteeing the energy bounds required for passivity. The effectiveness of the proposed design is validated via an experiment performed on a virtual teleoperated environment.

Keywords:Networked control systems, Optimal control, Linear systems Abstract: Fundamental limitations in networked control systems (NCS) have been researched for the last years with many stability results, from channel transmission minimal rate based on information theory, to minimal signal-to-noise (SNR). For the latter, it has been confirmed early on that the usual culprits increase the minimal SNR for stability, such as unstable plant poles, non-minimum phase (NMP) zeros, time delay, together with new ones such as communication channel bandwidth and colored transmission noise. In this work we specifically propose two approaches to completely avoid the effect of NMP zeros on the minimal SNR for stability in discrete-time. The first approach stems from the observation that the controller that achieves the minimal SNR for a minimum phase plant in discrete-time, has all its zeros located outside the unit circle (NMP zeros). Such observation allows us to characterize this set of NMP zeros as candidate NMP zeros of alternative plant models with the same unstable poles, which in turn will not increase the minimal SNR for stability above the expression imposed only by the plant unstable poles. Our second approach extends the set of possible NMP zeros that do not increase the SNR limitation to any location, by proposing the synthesis of a two-degree of freedom linear time invariant controller solution that achieves the minimal SNR for stability imposed only by the plant unstable poles.

Keywords:Networked control systems, Agents-based systems, Cooperative control Abstract: This paper considers a formation shape control problem for point agents in a two-dimensional ambient space, where the control is distributed, is based on achieving desired distances between nominated agent pairs, and avoids the possibility of reflection ambiguities. This has potential applications for large-scale multi-agent systems having simple information exchange structure. One solution to this type of problem, applicable to formations with just three or four agents, was recently given by considering a potential function which consists of both distance error and signed triangle area terms. However, it seems to be challenging to apply it to formations with more than four agents. This paper shows a hierarchical control strategy which can be applicable to any number of agents based on the above type of potential function and a formation shaping incorporating a grouping of equilateral triangles, so that all controlled distances are in fact the same. A key analytical result and some numerical results are shown to demonstrate the effectiveness of the proposed method.

Keywords:Networked control systems, Delay systems, Lyapunov methods Abstract: In this paper we propose small-gain theorems for the global asymptotic stability and the input-to-state stability, as well as for the related incremental properties, for a network of nonlinear discrete-time systems, affected by uncertain and time-varying delays.

Keywords:Networked control systems, Supervisory control, Hybrid systems Abstract: We consider supervisory control of nonlinear systems which are implemented on digital networks. In particular, two candidate controllers are orchestrated by a supervisor to stabilize the origin of the plant by following a dwell time logic, i.e. evaluating a control-mode switching rule at instants which are at least spaced by some dwell time interval. The plant, the controllers and the supervisor communicate via a network and the transmissions are triggered by a mechanism at the discrete sampling instants, which leads to periodic event-triggered control. Thus, there are possibly two kinds of events generated at the sampling instants: the control-mode switching event to activate another control law and the transmission event to update the control input. We propose a systematic design procedure for periodic event-triggered supervisory control for nonlinear systems. We start from a supervisory control scheme which robustly stabilizes the system in the absence of the network. We then implement it over the network and design event-triggering rules to preserve its stability properties. In particular, for each candidate controller, we provide a lower bound for the control-mode dwell time, design criterion to generate transmission events and present an explicit bound on the maximum sampling period with which the triggering rules are evaluated, to ensure stability of the whole system. We show that there exist relationships among the control-mode dwell time, a parameter used to define the transmission event-triggering condition and the bound of the sampling period. An example is given to illustrate the results.

Keywords:Networked control systems, Control over communications, Communication networks Abstract: In this paper, we study a wireless networked control system (WNCS) with N ge 2 sub-systems sharing a common wireless channel. Each sub-system consists of a plant and a controller and the control message must be delivered from the controller to the plant through the shared wireless channel. The wireless channel is unreliable due to interference and fading. As a result, a packet can be successfully delivered in a slot with a certain probability. A network scheduling policy determines how to transmit those control messages generated by such N sub-systems and directly influences the transmission delay of control messages. We characterize the stability condition of such a WNCS under the joint design of the control policy and the network scheduling policy by means of 2^N linear inequalities. We further simplify the stability condition into only one linear inequality for two special cases: the perfect-channel case where the wireless channel can successfully deliver a control message with certainty in each slot, and the symmetric-structure case where all sub-systems have identical system parameters.

Keywords:Networked control systems, Linear systems Abstract: In this paper, we investigate the problem of determining the structural controllability of leader-follower systems defined over directed graphs. We identify the notions of graph structural controllability and strong graph structural controllability in leader-follower systems on directed graphs. We show that accessibility is a necessary and sufficient condition for graph structural controllability over directed graphs. Next, we identify a sufficient and a necessary condition for strong graph structural controllability. Finally, we derive a sufficient condition for controllability when two graphs are cascaded. We present examples that illustrate the various concepts.

Keywords:Networked control systems, Fault detection, Distributed control Abstract: This paper presents a distributed attack-resilient state estimation scheme for continuous-time linear systems having redundant sensors when some of them are corrupted by adversaries. We first design a distributed state observer so that individual observers from each of output measurements communicate with their neighbors and cooperate to recover the full state of the system. Then, the observers are partitioned into disjoint groups and local monitoring systems are designed for each of them. Even though the system is not observable from measurements in each group, every influential attack is detected and identified by local monitors using only local information and local observer estimates within the local group, with the help of sensing redundancy. In process of local attack identification, a notion of sensor attack identifiability is introduced which does not require observability. Finally, all corrupted output measurements are removed from the observer communication and the distributed resilient state estimation is achieved.

Keywords:Networked control systems, Estimation, Kalman filtering Abstract: This paper studies the problem of remote state estimation in the presence of a passive eavesdropper. A sensor measures a linear plant's state and transmits it to an authorized user over a packet-dropping channel, which is susceptible to eavesdropping. Our goal is to design a coding scheme such that the eavesdropper cannot infer the plant's current state, while the user successfully decodes the sent messages. We employ a novel class of codes, termed State-Secrecy Codes, which are fast and efficient for dynamical systems. They apply linear time-varying transformations to the current and past states received by the user. In this way, they force the eavesdropper's information matrix to decrease with asymptotically the same rate as in the open-loop prediction case, i.e. when the eavesdropper misses all messages. As a result, the eavesdropper's minimum mean square error (mmse) for the unstable states grows unbounded, while the respective error for the stable states converges to the open-loop prediction one. These secrecy guarantees are achieved under minimal conditions, which require that, at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. Meanwhile, the user's estimation performance remains optimal. The theoretical results are illustrated in simulations.

Keywords:Stochastic systems, Linear systems Abstract: We address the problem of security for general partially observed linear stochastic systems, where some of the sensors and actuators may be malicious. We consider multiple-input-multiple-output linear stochastic systems that are under attack, where an arbitrary subset of its sensors and actuators are ``malicious." A malicious sensor need not report its measurements truthfully, and a malicious actuator need not apply inputs in accordance with the prescribed control policy. For any such system, we show that there exists a decomposition of the state space into two orthogonal subspaces, called the securable and the unsecurable subspaces, and design a test that can be used by the honest sensors and actuators, such that if the malicious activity is to remain undetected by this test, then the covariance of the projection of the state estimation error of the honest nodes on the securable subspace remains at its designed value regardless of what attack strategy the malicious sensors and actuators choose to employ. This test therefore guarantees that the malicious nodes can degrade the state estimation performance only along the unsecurable subspace of the linear dynamical system.

Keywords:Estimation, Linear systems, Networked control systems Abstract: With network-based attacks, such as Man-in-the-Middle (MitM) attacks, the attacker can inject false data to force a closed-loop system into any undesired state, unless even intermittently integrity of delivered sensor measurements is enforced. Yet, the use of standard cryptographic techniques that ensure data integrity, such as Message Authentication Codes (MACs), introduces significant communication and computation overhead. Thus, in this work we explore the use of cumulative MACs that significantly reduce network overhead. We consider systems with Kalman filter-based state estimators and sequential probability ratio test (SPRT) intrusion detectors. We show that strong estimation guarantees under MitM attacks can be obtained even with intermittent use of a single cumulative MAC that is added to appropriate sensor measurements transmitted over the network. We present a design-time methodology to evaluate the effects of any given cumulative integrity enforcement policy on reachable state-estimation errors for any type of stealthy attacks; this provides a base for the design of cumulative enforcement policies with desired performance guarantees even in the presence of MitM attacks. Finally, we illustrate the effectiveness of our approach on an automated steering control.

Keywords:Networked control systems, Sensor networks, Communication networks Abstract: The cyber-security of multi-agent control systems has become vital in practice. To protect the communication process between the individual agents over TCP/IP networks, one must encrypt the messages to be sent, which is costly in a large-scale network when high-level security is demanded. To lessen the burden of heavy encryption and decryption processes, we introduce the Homomorphic Encryption to reduce the number of encryption/decryption terminals that are supposed to equip with every agent. The security is enhanced by the quantum key distribution technology, which can generate secret keys that are theoretically absolutely secure even against quantum computation. We proposed a hybrid method that make good use of the randomness of quantum keys, one-time pad and symmetric encryption to make sure the overall security of homomorphic encryption algorithms. Numerical simulations are provided to illustrate how our scheme.

Keywords:Communication networks, Sensor networks, Network analysis and control Abstract: We investigate the connectivity of wireless sensor networks secured by the heterogeneous random pairwise key predistribution scheme. In contrast to the homogeneous scheme proposed by Chan et al., where each node is paired (offline) with K other nodes chosen uniformly at random; herein, each node is classified as class-1 with probability mu or class-2 with probability 1-mu, for 0