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.

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.

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 l₁-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.

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.

Keywords: Biomolecular systems, Stability of nonlinear systems, Uncertain systems
Abstract: Recent advances in nucleic acid-based chemistry have highlighted its potential for the implementation of biomolecular feedback circuits.

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.

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.

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.