Keywords:Network analysis and control, Stability of nonlinear systems, Large-scale systems Abstract: In recent work, we laid the basis of an analysis framework for the study of heterogeneous networks. In essence, it is postulated that in a heterogeneous network a collective non-trivial behaviour arises, which may be modelled as a dynamical system itself. Then, we say that the networked systems synchronize or, more precisely, achieve dynamic consensus if they adopt this emergent behaviour. In this paper we consider the case-study of coupled Andronov-Hopf oscillators. We establish that the emergent dynamics, which is of the same nature as a single oscillator, is orbitally stable. Then, we show that the trajectories of the individual oscillators tend to a neighbourhood of the stable orbit. For the first time in the study of synchronization, the analysis is based on singular-perturbations theory; we show that the emergent dynamics corresponds to a slow system while the synchronization errors form a fast dynamics.

Keywords:Network analysis and control, Stability of nonlinear systems, Optimization Abstract: A computer malware is a malicious code that compromises a node and then attempts to infect the node’s neighbors in order to mount further attacks. Strategies for mitigating malware propagation attacks are based on patching each node at a certain rate, which is selected based on a trade-off between removing the viruses and the cost of patching. This selection, however, implicitly assumes that the propagation rate is known, whereas in practice the propagation rate depends on the inherently uncertain goals and capabilities of the attacker. In this paper, we propose and analyze adaptive defense strategies against malware with unknown propagation rates from a control-theoretic perspective. We introduce a distributed defense strategy in which each host increases its patching rate when a malware is detected, and decreases its patching rate when the host is not infected. The proposed patching strategies can drive the probability of infection to an arbitrarily low value at steady-state by varying the patching update parameters. Using a passivity-based approach, we prove that, when each node has the same patching parameters, the adaptive defense strategy ensures that the infection probabilities converge to any desired positive steady-state value. When the parameters are heterogeneous among nodes, we prove local stability of the adaptive patching dynamics, analyze the convergence rate of the infection probability, and formulate an optimization problem for selecting the infection probabilities based on a trade-off between the cost of patching and the cost of infection at steady-state. Our results are illustrated through a numerical study.

Keywords:Network analysis and control, Stability of nonlinear systems, Power systems Abstract: We provide sufficient conditions for asymptotic stability and optimal resource allocation for a network preserved microgrid model formed by inverter-interfaced generation units together with constant active and reactive power loads. The model considers explicitly the presence of constant power loads as well as the coupling between the phase angle and voltage dynamics. The analysis of the resulting nonlinear differential algebraic equation (DAE) system is conducted by leveraging incremental Lyapunov functions, definiteness of the load flow Jacobian and the implicit function theorem.

Keywords:Network analysis and control, Transportation networks, Switched systems Abstract: The evolution of many networked systems, such as air transportation, can be modeled using a combination of the network topology and the resultant dynamics. In particular, time-varying networks can be represented by switching between candidate topologies. This paper models such systems as discrete-time, positive Markov Jump Linear Systems. Time-varying, periodic Markovian transition matrices and continuous state resets during discrete-mode transitions are also incorporated. Two notions of stability are considered: Mean Stability and Almost-Sure Stability, and appropriate conditions are derived for both of them. The analysis techniques are demonstrated using models determined from operational air traffic delay data. The results show that air traffic delay networks satisfy the proposed conditions for both mean stability and almost-sure stability, implying that delays tend to decay over time, even though several of the component discrete modes are unstable. Different nodes (airports) are also evaluated in terms of the persistence of delays and their susceptibility to network effects.

Keywords:Network analysis and control Abstract: This paper deals with an extended framework of the distributed asymptotic agreement problem by allowing the presence of unilateral interactions (optimistic or pessimistic) in place of bilateral ones, for a large class of nonlinear monotone time-varying networks. In this original setup we firstly introduce notions of unilateral optimistic and/or pessimistic interaction, of associated bicolored edge in the interaction graph and a suitable graph-theoretical connectedness property. Secondly, we formulate a new assumption of integral connectivity and show that it is sufficient to guarantee exponential convergence towards the agreement subspace. Finally, we remark that the proposed conditions are also necessary for consensuability. Theoretical advances are emphasized through illustrative examples given both to support the discussion and to highlight how the proposed framework extends all existing conditions for consensus of monotone networks.

Keywords:Network analysis and control Abstract: Reichert’s theorem (1969), a fundamental theorem of network synthesis, completely characterises minimum reactive synthesis of positive-real biquadratic impedances. The crucial part of the original approach depends on a complicated topological argument. This paper provides an alternative proof using the recently introduced concept of regular positive-real functions.

Keywords:Cooperative control, Agents-based systems Abstract: A distributed algorithm is described for finding a common fixed point of a family of m > 1 nonlinear maps M_i assuming that each map is a paracontraction. The common fixed point is asynchronously computed in real time by m agents assuming each agent i knows only M_i, the current estimates of the fixed point generated by its neighbors, and nothing more. Each agent recursively updates its estimate of the fixed point at its own event times, by utilizing estimates generated by each of its neighbors. Neighbor relations are characterized by a time-dependent directed graph mathbb N(t) whose vertices correspond to agents and whose arcs depict neighbor relations.

Keywords:Agents-based systems, Network analysis and control, Linear systems Abstract: This paper aims to achieve cluster synchronization for coupled linear dynamical systems whose models are distinct in different clusters under directed nonnegative graphs. Both static coupling strategies and dynamic coupling strategies are utilized. The static couplings are applicable to interaction graphs where the inter-cluster connections are acyclic, and will render the analysis intractable when inter-cluster connections form cycles. In comparison, the dynamic couplings are shown to be applicable in general graphs. A cluster spanning trees condition is imposed on the interaction graph, and is shown to be necessary and sufficient under acyclic inter-cluster structures. Lower bounds on a weighting factor of the interaction graph are derived under the two coupling strategies, respectively.

Keywords:Agents-based systems, Networked control systems, Simulation Abstract: The classic Hegselmann-Krause (HK) model for opinion dynamics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of the agents within a fixed distance R. In this work, we investigate the effects of noise in the continuous-time version of the model as described by its mean-field Fokker-Planck equation. In the presence of a finite number of agents, the system exhibits a phase transition from order to disorder as the noise increases. We introduce an order parameter to track the phase transition and resolve the corresponding phase diagram. The system undergoes a phase transition for small R but none for larger R. Based on the stability analysis of the mean-field equation, we derive the existence of a forbidden zone for the disordered phase to emerge. We also provide a theoretical explanation for the well-known 2R conjecture, which states that, for a random initial distribution in a fixed interval, the final configuration consists of clusters separated by a distance of roughly 2R. Our theoretical analysis confirms previous simulations and predicts properties of the noisy HK model in higher dimension.

Keywords:Agents-based systems, Optimal control, Computational methods Abstract: The problem of achieving minimum time consensus for an N-agent system, with double integrator agents having bounded inputs, is considered. At the initial time instant, each agent has access to the state information about all the other agents. An algorithm, of O(N^2) complexity, is proposed to compute the final consensus target state and minimum time to achieve this consensus. Further, local control laws are synthesized to drive each agent to the target point in the computed minimum time to consensus.

Keywords:Agents-based systems, Sensor networks, Cooperative control Abstract: This paper considers dynamic coverage control of unicycle multi-agent systems under power constraints. The agents under consideration model a visually based patrol protocol. They observe their environment via forward-facing conical anisotropic sensing regions. A local coverage control strategy is presented that allows for the cooperative search of a domain while maintaining collision avoidance guarantees using a novel control method based on the coverage level. Additionally, a novel energy-aware global coverage technique is introduced that restricts the operating range of power- constrained agents while shifting the network redistribution effort onto less constrained agents. The results of several scenarios are presented in simulation to illustrate the efficacy of these algorithms.

Keywords:Agents-based systems, Kalman filtering, Distributed control Abstract: Localization and tracking of a moving target has been established as a key problem in wireless sensor networks, with many algorithms being proposed in this area. In particular, time-difference of arrival (TDOA) localization is considered to be a cost-effective and accurate localization technique. However, traditional TDOA algorithms rely on a central node that produces an estimate of the target's location by gathering measurements from all other nodes in the network. In this work, we solve the problem by distributing the estimation among all agents in the network, avoiding problems posed by the centralized approach, such as single-node failure. Each agent in the network runs its own extended Kalman filter (EKF) in order to estimate the target's position, while a neighbor-based averaging procedure is proposed to facilitate the consensus of agents' estimates. This approach does not require each node to fully observe the process, i.e., some nodes in the network may have an insufficient number of neighbors to accurately estimate the target's position on their own. We show that the estimation error is bounded, with a numerical example illustrating the performance of the proposed algorithm.

Keywords:Cooperative control, Networked control systems, Communication networks Abstract: Compositional barrier functions are proposed in this paper to systematically compose multiple objectives for teams of mobile robots. The objectives are first encoded as barrier functions, and then composed using AND and OR logical operators. The advantage of this approach is that compositional barrier functions can provably guarantee the simultaneous satisfaction of all composed objectives. The compositional barrier functions are applied to the example of ensuring collision avoidance and static/dynamical graph connectivity of teams of mobile robots. The resulting composite safety and connectivity barrier certificates are verified experimentally on a team of four mobile robots.

Keywords:Cooperative control, Networked control systems, Decentralized control Abstract: Our goal is to design decentralized coordination strategies that enable agents to achieve global performance guarantees while minimizing the energy cost of their actions with an emphasis on feasibility for real-time implementation. As a motivating scenario that illustrates the importance of introducing energy awareness at the agent level, we consider a team of mobile nodes that are assigned the task of establishing a communication link between two base stations with minimum energy consumption. We formulate this problem as a dynamic program in which the total cost of each agent is the sum of both mobility and communication costs. To ensure that the solution is decentralized and real time implementable, we propose multiple suboptimal policies based on the concepts of approximate dynamic programming. To provide performance guarantees, we compute upper bounds on the performance gap between the proposed suboptimal policies and the global optimal policy. Finally, we discuss merits and demerits of the proposed policies and compare their performance using simulations.

Keywords:Cooperative control, Networked control systems, Distributed control Abstract: This paper concerns Leader-following consensus problem of multi-agent systems with Markovian switching topology. In order to reduce the amount of transmission data and decrease the frequency of controller update simultaneously, a novel event-triggered control strategy is proposed. Partly information exchange among agents and channel noise are considered to describe the environment uncertainties in practical. It has been shown that by using the proposed control scheme, the overall agents could achieve H_{infty} leader-following consensus. Finally, an example is given to show the effectiveness of the main result.

Keywords:Cooperative control, Networked control systems, Linear systems Abstract: This paper investigates output H_{infty} synchronization of a group of linear heterogeneous agents. Agents are subject to external unmodeled disturbances and distributively communicate one set of outputs. The aim is to design a distributed controller to achieve synchronization on another set of outputs with an H_{infty} bound. We obtain an H_{infty}-criterion for each agent that guarantees output synchronization in the absence of the external unmodeled disturbances and output H_{infty} synchronization in their presence. We derive the overall mathcal{L}_2-gain of the output synchronization error with respect to the external unmodeled disturbances. We demonstrate our developments by a simulation example.e.

Keywords:Cooperative control, Networked control systems, Network analysis and control Abstract: This paper deals with a cooperative control problem of networked heterogeneous input-output passivity-short (PS) multi-agent systems in a sampled-data setting. The dynamics of each system are continuous, whereas the exchange of information on a communication network is operated in a discrete-time manner. The analysis and cooperative control design are transformed into representative forms of discretized systems using a zero-order holder and an ideal sampler. Based on the concept of PS, a design of a distributed static output feedback control for achieving output consensus is proposed. Compared with the concept of passivity, it is shown that PS extends the systems under consideration to higher relative degree and/or non-minimum phase. This extension allows the design of a distributed controller by quantifying the impact of each system in networked operation. Furthermore, properties of PS are discussed both in the continuous and discrete-time domain, and conditions for preserving PS through discretization are presented.

Keywords:Robotics, Decentralized control Abstract: Standard centralized motion controllers for robotic systems require precise model structure for manipulator dynamics. The controlled robot is also sensitive to sensor failure as each joint in robot receives information from sensors of all other joints. In this paper, we present a dynamically smooth adaptive decentralized controller for robotic manipulators where the control law in each joint depends only on local measurements from that joint. The use of possibly un-calibrated joint torque sensors eliminates the need for modeling link dynamics. Global and asymptotic motion tracking is achieved. Simulation examples demonstrate significant improvement in robustness of the controlled system in face of sensor failure.

Keywords:Kalman filtering, Large-scale systems, Sensor networks Abstract: In this paper, we focus on batch state estimation for linear systems. This problem is important in applications such as environmental field estimation, robotic navigation, and target tracking. Its difficulty lies on that limited operational resources among the sensors, e.g., shared communication bandwidth or battery power, constrain the number of sensors that can be active at each measurement step. As a result, sensor scheduling algorithms must be employed. Notwithstanding, current sensor scheduling algorithms for batch state estimation scale poorly with the system size and the time horizon. In addition, current sensor scheduling algorithms for Kalman filtering, although they scale better, provide no approximation performance guarantees on the minimization of the batch state estimation error. In this paper, one of our main contributions is to provide an algorithm that enjoys both the estimation accuracy of the batch state scheduling algorithms and the low time complexity of the Kalman filtering scheduling algorithms. In particular: 1) our algorithm is near-optimal: it achieves a solution up to a multiplicative factor 1/2 from the optimal solution, and this factor is close to the best approximation factor 1/e one can achieve in polynomial time for this problem; 2) our algorithm has (polynomial) time complexity that is not only lower than that of the current algorithms for batch state estimation; it is also lower than, or similar to, that of the current algorithms for Kalman filtering. We achieve these results by proving two properties for our batch state estimation error metric, which quantifies the square error of the minimum variance linear estimation of the batch state vector: a) it is supermodular in the choice of the selected sensors; b) it has a sparsity pattern (it involves matrices that are block tri-diagonal) that facilitates its evaluation at each sensor set.

Keywords:Control of networks, Network analysis and control, Networked control systems Abstract: Quantifying controllability in large dynamical networks and designing network structures with good controllability properties has generated significant recent interest. We consider actuator placement problems in dynamical networks and show that the mappings from actuator subsets to four fundamental optimal control metrics are in general neither supermodular nor submodular set functions via a simple counterexample. We also find a set of restrictive conditions under which these mappings are modular set functions. Although this implies that simple greedy algorithms do not in general produce actuator placements with guaranteed near optimal closed-loop control performance, we find in computational experiments that greedy algorithms can exceed performance and far exceed scalability of convex relaxation heuristics with general purpose semidefinite programming solvers.

Keywords:Network analysis and control, Observers for Linear systems, Fault tolerant systems Abstract: We study the problem of distributed state estimation of a linear time-invariant system by a network of nodes, some of which are subject to adversarial attacks. We develop a secure distributed estimation strategy subject to an f-locally bounded Byzantine adversary model, where a compromised node can arbitrarily deviate from the rules of any prescribed algorithm. Under such a threat model, we provide sufficient conditions guaranteeing the success of our estimation strategy. Our method relies on the construction of a subgraph, which we call a Mode Estimation Directed Acyclic Graph (MEDAG), for each unstable and marginally stable eigenvalue of the plant. We provide a distributed algorithm for constructing a MEDAG and characterize graph topologies for which the construction algorithm is guaranteed to succeed. Our approach provides fundamental insights into the relationship between the dynamics of the system, the measurement structure of the nodes, and the underlying graph topology.

Keywords:Network analysis and control, Control of networks, Optimal control Abstract: We study the problem of leader selection in directed consensus networks. In this problem, certain `leader' nodes in a consensus network are equipped with absolute information about their state. This corresponds to diagonally strengthening a dynamical generator given by the negative of a directed graph Laplacian. We provide a necessary and sufficient condition for the stabilization of directed consensus networks via leader selection and form regularized H2 and H-infinity optimal problem leader selection problems. We draw on recent results that establish the convexity of the H2 and H-infinity norms for structured decentralized control of positive systems and identify sparse sets of leaders by imposing an l1 penalty on the vector of leader weights. This allows us to develop a method that simultaneously assigns leader weights and selects a limited number of leaders. We use proximal gradient and subgradient method to solve the optimization problems and provide examples to illustrate our developments.

Keywords:Networked control systems, Communication networks, Computational methods Abstract: We investigate the effects of random and malicious packet losses on the stability of a networked control system. Specifically, we explore the networked control problem for the case where the plant and the controller exchange state and control input packets over a communication channel that may face random transmission failures as well as malicious attacks by an intelligent agent. We obtain a sufficient condition for the stability of the networked system and show that this condition can be assessed by examining the solutions to linear programming problems. The coefficients of the constraints in these problems depend on an asymptotic upper-bound for the average number of transmission failures that we use for characterizing random packet losses and malicious attacks. We illustrate the efficacy of our results with a numerical example.

Keywords:Networked control systems, Communication networks, Optimization algorithms Abstract: We investigate the scenario where a controller is connected to a plant using a wireless network. Our objective is to design control strategies, which efficiently use the network in terms of energy, by taking into account the fluctuations of the wireless channel. In particular, we consider discrete-time systems and we focus on time-triggered control. That is, we assume that we know a controller, which ensures a desired property (such as stability), as long as two successive transmissions are not spaced by more than a fixed number of steps N. The problem formulation is generic in the sense that we do not make any assumption on the plant and the controller structures or properties, all we need to ensure is the constraint on the transmission times. We then present triggering strategies to minimize the energy expenditure based on knowledge on the channel state, while ensuring that two successive transmissions are not spaced by more than N steps. The results demonstrate that periodically communicating after exactly N time instants has passed (to minimize the number of transmissions), is not always the optimal scheme to minimize the energy cost. As a result of certain properties of the wireless channel, communicating more often when the wireless channel conditions are good, results in a smaller energy consumption overall despite a higher frequency of communication. Numerical results confirm the validity of the approach and show that a significant amount of energy can be saved.

Keywords:Predictive control for linear systems, Estimation Abstract: We propose a novel output feedback model predictive control scheme for linear discrete-time systems incorporating a set-valued estimator based on a ﬁxed ﬁnite number of recent measurements. Recursive feasibility is established by basing predictions that are farther in the future on fewer measurements. The resulting optimization problem is convex with linear constraints. We demonstrate in a numerical example that the proposed model predictive control scheme allows an enlargement of the feasible set beyond what is possible with earlier schemes using linear estimators.

Keywords:Predictive control for linear systems, Differential-algebraic systems, Robust control Abstract: In this paper we propose to apply a novel economic robust predictive controller for periodic signals following a constraint tightening procedure to an uncertain discrete time algebraic-differential linear model of a community micro-grid. The system considered has been obtained from the power balance equations of three nano-grids taking into account bounded additive perturbations. In this model, we assume that a prediction of the of the generation and local load is available and that its prediction error is bounded. This controller joins dynamic and economic trajectory planning and robust predictive controller for tracking in a single layer taking into bounded disturbances, algebraic constraints and the periodic character of the system.

Keywords:Stochastic optimal control, Predictive control for linear systems, Identification for control Abstract: The closed-loop performance of model-based controllers often degrades over time due to increased model uncertainty. Some form of model maintenance must be performed to regularly adapt the system model using closed-loop data. This paper addresses the problem of control-oriented model adaptation in the context of predictive control of stochastic linear systems. A stochastic predictive control approach is presented that integrates stochastic optimal control with control-oriented input design in order to confer some degree of probing effect to the control inputs. The probing effect will enable generating informative closed-loop data for (online) control-oriented model maintenance. In a simulation study, the performance of the proposed stochastic predictive control approach with integrated input design is demonstrated on a atmospheric-pressure plasma jet with potential biomedical applications.

Keywords:Stochastic systems, Predictive control for nonlinear systems, Constrained control Abstract: This paper presents a model predictive control scheme for a class of stochastic nonlinear systems subject to chance constraints. The applied control is composed of a nominal control action which is based on the solution of a tightened deterministic optimal control problem and an ancillary control law. The ancillary control law fights the uncertainties in between sampling times. Chance constraints satisfaction as well as convergence in a probabilistic sense of the closed loop system are discussed. The overall approach is only slightly more computational expensive than the corresponding nominal, deterministic model predictive controller. The approach is illustrated by a numerical example.

Keywords:Switched systems, Stochastic optimal control, Markov processes Abstract: In this paper, we address finite-horizon optimal control of Markov Jump Linear Systems with non-observed discrete-valued system state via dynamic output feedback. It has been shown that the optimal control law for this problem is intractable. For this reason, we assume a mode-independent control policy consisting of a linear time-variant estimator that reconstructs the continuous-valued state from noisy measurements, and a linear time-variant regulator that maps the state estimate to control inputs. To the best of our knowledge, this problem remained unsolved because even under the assumption of a linear control law, the separation between the estimator and the regulator does not hold. However, by minimizing an upper bound on the true costs induced by the control, we are able to design an iterative algorithm for computation of the controller parameters whose convergence is shown. The proposed algorithm is demonstrated by means of a simulation.

Keywords:Optimal control, Robust control, Predictive control for nonlinear systems Abstract: The use of detailed models over long horizons in predictive control can be computationally challenging. Furthermore, always-present uncertainty renders the use of such sophisticated detailed models over long time horizons questionable due to the resulting variability of the trajectories. We propose a multi-stage scheme that combines the use of models of different granularity -- using detailed models for short-term predictions, while performing long-term predictions with less detailed models. Using projection and invariance properties for the different model complexities and the transitions between them, we show that this scheme is recursively feasible. In a simulation study, we show how two models of different complexity can be combined for steering a mobile robot through a landscape with obstacles.

Keywords:Large-scale systems, Decentralized control, Optimal control Abstract: In previous work, we proposed the localized linear quadratic regulator (LLQR) method as a scalable way to synthesize and implement distributed controllers for large-scale systems. The idea is to impose an additional spatiotemporal constraint on the closed loop response, which limits the propagation of dynamics to user-specified subsets of the global network. This then allows the controller to be synthesized and implemented in a localized, distributed, parallel, and thus scalable way. Nevertheless, the additional spatiotemporal constraint also makes the LLQR controller sub-optimal to the traditional centralized one. The goal of this paper is to quantify and bound the suboptimality of the LLQR controller introduced by the additional spatiotemporal constraint. Specifically, we propose an algorithm to compute a lower bound of the cost achieved by the centralized controller using only local plant model information. This allows us to determine the sub-optimality of the LLQR controller in a localized way, and adaptively update the LLQR constraint to exploit the tradeoff between controller complexity and closed loop performance. The algorithm is tested on a randomized heterogeneous network with 51200 states, where the LLQR controller achieves at least 99% optimality compared to the unconstrained centralized controller.

Keywords:Quantum information and control, Large-scale systems, Optimal control Abstract: Optimal control is one of the most popular and efficient control strategies that have been widely used in both classical and quantum systems. Inspired by the recent progresses of quantum algorithms, we find that optimal control protocols can be exponentially accelerated by embedding a quantum controller in the control loop instead of the classical controller. This is the first time to our knowledge that a quantum controller has been shown to exponentially improve the efficiency of control compared with classical controller. Our method opens up new perspectives in various fields, especially those related to the synthesis of large-scale complex systems.

Keywords:Mean field games, Optimal control, Numerical algorithms Abstract: We study a crowd model proposed by R. Hughes in cite{hug02} and we describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two examples.

Keywords:Machine learning, Optimal control, Evolutionary computing Abstract: This paper addresses the problem of deriving a policy from the value function in the context of reinforcement learning in continuous state and input spaces. We propose a novel method based on genetic programming to construct a symbolic function, which serves as a proxy to the value function and from which a continuous policy is derived. The symbolic proxy function is constructed such that it maximizes the number of correct choices of the control input for a set of selected states. Maximization methods can then be used to derive a control policy that performs better than the policy derived from the original approximate value function. The method was experimentally evaluated on two control problems with continuous spaces, pendulum swing-up and magnetic manipulation, and compared to a standard policy derivation method using the value function approximation. The results show that the proposed method and its variants outperform the standard method.

Keywords:Maritime control, Optimal control, Kalman filtering Abstract: This paper presents a solution to the problem of Dynamic Positioning of vessels in Arctic environments, using a finite-horizon optimal control based approach. As the first step, an Unscented Kalman Filter (UKF) based non-linear observer is developed for estimating both the vessel states and unknown inputs such as ice load. To perform better set point control and disturbance rejection, a Non-linear Model Predictive Controller (NMPC) is employed for dynamic positioning. Using the developed estimation and control strategies, successful simulation results are obtained. Furthermore, the optimum control module is integrated with a commercial vessel manoeuvring software and promising real-time results are generated.

Keywords:Network analysis and control, Stability of nonlinear systems, Decentralized control Abstract: We present guidelines for multi-agent coordination in dynamic networks. Using a contraction approach, we derive a connection between an agent’s intra-dynamics and those of its neighboring agents. We introduce the notion of epsilon-coordination to quantify how well agents are being coordinated to collectively regulate a network and we present a necessary and sufficient condition for the existence of epsilon-coordination schemes. We show that this condition manifests as a linear feasibility problem and we then investigate many implications of our main result. We conclude by using our main result to regulate a 6-agent network.

Keywords:Optimization algorithms, Optimization, Numerical algorithms Abstract: The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally demanding, especially for large-scale problems. This paper presents a new algorithm which is more computationally efficient, since it does not require either additional optimization variables or computation of the Hessian matrix. It is proven that the proposed algorithm converges locally to a solution of the KKT optimality conditions. An application example is presented to demonstrate the effectiveness of the proposed algorithm.

Keywords:Optimization algorithms, Optimization, Predictive control for nonlinear systems Abstract: Sequential Quadratic Programming (SQP) denotes an established class of methods for solving nonlinear optimization problems via an iterative sequence of Quadratic Programs (QPs). Several approaches in the literature have established local and global convergence of the method. This paper considers a variant to SQP that, instead of solving each QP, at each iteration follows one gradient step along a direction that is proven to be a descent direction for an augmented Lagrangian of the nonlinear problem, and in turn is used to generate the next QP. We prove global convergence to a critical point of the original nonlinear problem via a line search that requires the same assumptions as the SQP method.

The method is then applied to nonlinear Model Predictive Control (MPC). To simplify the problem formulation and achieve faster convergence, we propose a locally convergent reformulation. An important speed-up is observed in practice via a specific initialization. The computational efficiency of the proposed method is finally shown in a numerical example.

Keywords:Optimization, Optimization algorithms Abstract: The paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem. Specifically, we propose a novel matrix-scaling of the partial derivatives that acts as an efficient preconditioning for the standard stochastic gradient descent algorithm. This proposed matrix-scaling provides a trade-off between local and global second order information. It also resolves the issue of scale invariance that exists in matrix factorization models. The overall computational complexity is linear with the number of known entries, thereby extending to a large-scale setup. Numerical comparisons show that the proposed algorithm competes favorably with state-of-the-art algorithms on various different benchmarks.

Keywords:Pattern recognition and classification, Optimization algorithms, Machine learning Abstract: We consider a class of multi-parametric quadratic programming (mpQP) that is closely related with large margin learning methods in data mining. With a new treatment for two types of constraints, we derive the parametric solution and provide further results on the geometric structure of the optimality. The issue of degeneracy is discussed in some depth: We show that primal degeneracy can be naturally avoided with the new treatment, and that a classification property composes a sufficient condition to rule out dual degeneracy. For general mpQP that is not strictly convex, a decomposition method is proposed based on null space technique. The theoretical analyses are then connected to large margin machine learning: it is shown that the problem of model selection can be directly reduced to the corresponding mpQP. Moreover, we demonstrate that the problem of learning with hidden variables can be transformed into a concave minimization, which admits diverse global optimization algorithms. Finally, experiments are conducted on publicly available datasets to empirically test the two applications.

Keywords:Optimization algorithms, Pattern recognition and classification, Simulation Abstract: Undersampling is a simple but efficient way to increase the imaging rate of atomic force microscopy (AFM). The undersampled AFM images typically can be faithfully reconstructed with signal recovery techniques such as inpainting or algorithms from compressive sensing. In this paper, we consider the case when the dynamic processes of the sample occur in a small proportion of the entire scanning area of AFM while the background is relatively static and only slowly changing. In this setting, two consecutive video frames, termed the reference frame and the target frame, share a significant amount of static regions in common. Based on the measurements, we use greedy algorithms to select measured pixels in the reference frame that are likely to be from the common static regions and share them to the target frame. The target frame can then be reconstructed from both the original and shared pixels, yielding a more accurate reconstruction. This algorithm is then extended to the more realistic problem of multiple frames. Through simulation, we demonstrate that the proposed algorithm can achieve better overall video reconstruction quality compared to the frame-to-frame based single image reconstruction.

Keywords:Optimization algorithms, Power electronics, Numerical algorithms Abstract: In this paper the problem of maximum power point tracking (MPPT) is considered. We show that the problem has a unique solution and it can be reduced to the problem of finding the unique root of a single variable scalar function. We show that Newton's iterations can be applied to the problem of finding this root quadratically fast for an initialisation that is independent of the parameters of the MPPT problem. The results of applying the approach to 1,000,000 randomly-generated instances of the MPPT problem are presented and consistency with the analysis is observed.

Keywords:Stochastic systems, Agents-based systems, Biological systems Abstract: In this work, we discuss the feasibility of motion camouflage in the two agent planar pursuit problem in which the pursuer implements a feedback strategy employing delayed sensory information subject to noise, whose variance is inversely proportional to the delay. This variance-delay modeling assumption is intended to capture the tradeoff between the speed of computation and accuracy of information available to the pursuer. However, in this paper, we limit ourselves to fixed variance and a range of delays.

Keywords:Stochastic systems, Algebraic/geometric methods, Simulation Abstract: Several engineering applications require numerical schemes for the simulation of stochastic differential equations (SDEs) on the Stiefel manifold of n × p real matrices with orthonormal columns (n ≥ p). The geometry of the Stiefel manifold causes classical schemes to fail, as they leave the manifold after one time step. Motivated by deterministic schemes on the Stiefel manifold, we develop a scheme for SDEs which always remains on the manifold. Our scheme can be easily applied to any SDE on the Stiefel manifold. The derivation is direct and made accessible to an engineering audience. Simulations with n = 1000, p = 10 are provided.

Keywords:Stochastic systems, Networked control systems, Linear systems Abstract: In order to conceal the information of the state of a given system, this paper adds an artificial noise called a privacy input to the state. The privacy input is designed as a Gaussian random variable with the mean zero and the time varying variance, i.e., the variance is a design variable. In order to measure confidentiality of the state, the paper uses the mutual information of the state and the output which is the perturbed state by the privacy input. The article formulates a problem which finds all controllers such that a given linear scalar system is mean square asymptotically stable and satisfies a given confidential level of the state. Simulation results demonstrate that solutions of the problem are useful to conceal the information of the transient state.

Keywords:Stochastic systems, Distributed control, Estimation Abstract: In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as independent control inputs. We analyze the diffusion-based control strategy using standard operator semigroup-theoretic arguments. We show that the diffusion coefficient can be chosen to be dependent only on the robots' local measurements to ensure that the swarm density converges to a function proportional to the scalar field. The boundedness of the domain precludes the need to impose assumptions on decaying properties of the scalar field at infinity. Moreover, exponential convergence of the swarm density to the equilibrium follows from properties of the spectrum of the semigroup generator. In addition, we use the proposed coverage method to construct a time-inhomogenous diffusion process and apply the observability of the heat equation to reconstruct the scalar field over the entire domain from observations of the robots' random motion over a small subset of the domain. We verify our results through simulations of the coverage scenario on a 2D domain and the field estimation scenario on a 1D domain.

Keywords:Stochastic systems, Estimation, Kalman filtering Abstract: Estimation of state, parameter and disturbances in dynamical system is a consistently investigated issue worldwide. In this paper we propose the Field Kalman Filter - a method for realization of this task in linear stochastic systems. In particular we prove, using Bayes' theorem, the formulas describing probability distributions of investigated quantities. Additionally we give an approximate implementation based on moving horizon approach. Efficiency of the method is illustrated with a particle tracking problem and by comparing it to competitive approaches - ALS and direct Bayesian estimation.

Keywords:Finance, Stochastic systems, Delay systems Abstract: This paper is part of a new line of research involving the use of a model-free controller to trade stock. The main result is a discrete-time version of the so-called Robust Positive Expectation Theorem which includes delay in the controller. To date, no results in the literature are available for this delay case. Motivated by robustness considerations and consistent with existing work, neither modelling nor identification of the stock price dynamics is involved. The time-varying investment level is generated using a "hard-wired" feedback controller which processes cumulative gains and losses. While this paper addresses discrete time, it is noted that the results also apply to high-frequency trading since the discretization interval Δt is allowed to be arbitrarily small.

King Fahad Univ. of Petroleum & Minerals, Dhahran, Saudi Ar

Keywords:Estimation, Modeling, Computational methods Abstract: A novel procedure is suggested to jointly identify the order of a GPR discrete relaxation spectrum and estimate its parameters (relaxation frequencies and their strengths). These quantities are important for interpreting the contents of the subsurface layers. The suggested method is capable of blindly identifying the number of relaxation modes and estimate their values and strengths. The procedure is hardware-friendly and exhibit high resistance to noise.

Keywords:Estimation, Nonlinear systems identification, Computational methods Abstract: We present a method of computing optimal input trajectories for parameter estimation in nonlinear dynamical systems using dynamic programming. In contrast with previously published dynamic programming formulations, we avoid adding an equation for the dispersion to the system state, allowing for more efficient solutions. This method is applicable whenever the design metric is linear in the Fisher information and is applicable to a general class of noise models. We implement this algorithm in the Julia programming language, and exploit parallelism to increase computation speed. A motivating application for this investigation is the design of dynamic acquisition sequences for magnetic resonance imaging (MRI). We also benchmark the performance of our parallel implementation on a low-dimensional population dynamics model.

Keywords:Estimation, Predictive control for nonlinear systems, Nonlinear systems identification Abstract: This paper proposes a discussion on the classification of the formulations of nonlinear Moving Horizon Estimators (MHE) of the literature into two categories: deterministic and stochastic. The stability of the dynamics of the estimation error is discussed for the MHEs in both frameworks. This paper also provides full explicit formulation of the stability conditions for the MHE in the deterministic framework, which were not given in the literature. Furthermore, robustness of MHE in both frameworks with respect to model errors is investigated through a simulation example of space object tracking. Comparison with other more classical estimators such as EKF, UKF and particle filter is also achieved.

Keywords:Estimation, Predictive control for nonlinear systems, Optimization Abstract: The computational effort may result in an overwhelming issue that prevents to use moving-horizon state estimation in a wide range of applications. Thus, in this paper we investigate the potential of moving-horizon estimators that provide an estimate of the state variables after performing a simple descent step based on the gradient or Newton methods. The stability analysis usually drawn in the case of exact minimization of the cost function cannot be applied. Thus, novel conditions on the stability of the estimation error for moving-horizon estimation based on single or multiple iterations of the gradient and Newton algorithms are derived for discrete-time linear and nonlinear noise-free systems. In the case of the gradient method for nonlinear systems, global exponential stability of the estimation error can be ensured. By contrast, only local stability is proved for the Newton-based approach. Under linear assumptions, also the error given by this estimator is demonstrated to be globally exponentially stable. The theoretical results are verified also by means of simulations, with a chaotic nonlinear system used as a testbed to estimate all the state variables only by means of measurements of the first one. The simulation results show that the gradient and Newton-based approaches perform quite well as compared with the extended Kalman filter.

Keywords:Robotics, Estimation, Pattern recognition and classification Abstract: The Simultaneous Localization and Mapping problem (SLAM) in robotics is typically modeled as a dyadic graph of relative pose measurements taken by the robot. The graph nodes store the values representing the absolute pose of the robot at a given point of time. An edge connecting two nodes represents robot movement and it stores the measurements taken by the robot sensor while moving between two nodes. The objective of the SLAM problem is to find the optimal global measurements best satisfying the noisy relative measurements. This problem of optimal estimation on a graph given relative measurements is a well-studied problem within the control community, for which several results and algorithms are known SLAM is generally solved as a least squares problem. Robust kernels which are less sensitive to outliers are used to deal with noise and outlier measurements. However, robust kernels tend to be dependent on initialization and can fail as the number of outliers increase. Therefore, it's important to identify and prune the outlier (noisy) measurements represented by incorrect loop closure edges for an accurate pose estimate.

In this paper we propose a multi-scale Heat-Kernel analysis based loop closure edge pruning algorithm for the SLAM graph. We show that compared to other pruning algorithms, our algorithm has a substantially higher precision and recall when compared and is able to handle a large amount of outlier measurements. We have corroborated results on several publicly available datasets and several types of noise. Our algorithm is not restricted to SLAM graphs only, but has a much wider applicability to other types of geometric graphs.

Keywords:Estimation, Sensor networks, Filtering Abstract: In this paper, the problem of distributed state estimation using networked local sensors is studied. Our previously proposed algorithm [1], [2] is further extended to the scenario where the underlying model of the state of interest is not known to each agent. Instead the underlying model belongs to a finite set of possible models known to all agents, and switches over time. The switching process follows a homogeneous Markov chain with known transition probabilities. Two algorithms are derived from our previous algorithm by following the frameworks of two well-known multiple model (MM) approaches, namely, the first order generalized pseudo Bayesian and interacting MM approaches. The proposed algorithms have the advantages of being fully distributed and robust against agents not directly sensing the target. More importantly, they require the agents to communicate only once during each sampling interval and hence decrease the burdens in communication. It is also shown for a special case when the underlying model is fixed, all local agents asymptotically identify the true model under certain conditions.

Keywords:Identification, Reduced order modeling, Linear systems Abstract: This paper deals with the problem of finding a low-complexity estimate of the impulse response of a linear time-invariant discrete-time dynamic system from noise-corrupted input-output data. To this purpose, we introduce an identification criterion formed by the average (over the input perturbations) of a standard prediction error cost, plus a weighted l1 regularization term which promotes sparse solutions. While it is well known that such criteria do provide solutions with many zeros, a critical issue in our identification context is where these zeros are located, since sensible low-order models should be zero in the tail of the impulse response. The flavor of the key results in this paper is that, under quite standard assumptions (such as i.i.d. input and noise sequences and system stability), the estimate of the impulse response resulting from the proposed criterion is indeed identically zero from a certain time index (named the leading order) onwards, with arbitrarily high probability, for a sufficiently large data cardinality. Numerical experiments are reported that support the theoretical results, and comparisons are made with some other state-of-the-art methodologies.

Keywords:Identification, Sensor networks, Estimation Abstract: This paper considers the identification of FIR systems, where the inputs and outputs of the system undergoes quantization into binary values before transmission to the system identifier. Provided that the thresholds of the input and output quantizers can be adapted, we propose identification schemes which are strongly consistent for Gaussian distributed inputs and noises. Identification schemes are given both for the case where the mean and variance of the input distribution are known, and when they are unknown.

Keywords:Identification, Statistical learning, Estimation Abstract: The problem of learning the parameters of a vector autoregressive (VAR) process from partial random measurements is considered. This setting arises due to missing data or data corrupted by multiplicative bounded noise. We present an estimator of the covariance matrix of the evolving state-vector from its partial noisy observations. We analyze the non-asymptotic behavior of this estimator and provide an upper bound for its convergence rate. This expression shows that the effect of partial observations on the first order convergence rate is equivalent to reducing the sample size to the average number of observations viewed, implying that our estimator is order-optimal. We then present and analyze two techniques to recover the VAR parameters from the estimated covariance matrix applicable in dense and in sparse high-dimensional settings. We demonstrate the applicability of our estimation techniques in joint state and system identification of a stable linear dynamic system with random inputs.

Istituto Italiano Di Tecnologia and Univ. Degli Studi Di Ge

Keywords:Identification, Statistical learning, Mechanical systems/robotics Abstract: This paper presents a semi-parametric algorithm for online learning of a robot inverse dynamics model. It combines the strength of the parametric and non-parametric modeling. The former exploits the rigid body dynamics equation, while the latter exploits a suitable kernel function. We provide an extensive comparison with other methods from the literature using real data from the iCub humanoid robot. In doing so we also compare two different techniques, namely cross validation and marginal likelihood optimization, for estimating the hyperparameters of the kernel function.

Keywords:Identification, Subspace methods, Closed-loop identification Abstract: The applicability of subspace-based system identification methods highly depends on the disturbances acting on the system. It is well-known, e.g., that the standard implementations of the MOESP, N4SID or CVA algorithms yield biased estimates when closed-loop noisy data is considered. In order to bypass this difficulty, we follow the recent trends for closed-loop subspace-based model identification and suggest, in a first step, pre-estimating the innovation term from the available data. By doing so, the initial subspace-based identification problem can be written as a deterministic problem for which efficient methods exist. Once the innovation sequence is estimated, the second step of our subspace-based identification procedure focuses on the estimation of the open-loop and closed-loop system's Markov parameters. A constrained least-squares solution is more precisely considered to guarantee structural constraints satisfied by Toeplitz matrices involved the open-loop and closed-loop data equations, respectively. The performance of the methods is illustrated through the study of simulation examples under open-loop and closed-loop conditions.

Keywords:Identification, Switched systems, Hybrid systems Abstract: We consider the problem of a real-time identification of switched linear systems in the presence of bounded noise. This is a challenging problem that involves the association of each data to the most suitable sub-system and the estimation of the parameters of all sub-systems. The proposed algorithm is based on an Outer Bounding Ellipsoid (OBE) type algorithm appropriate for real-time system identification with bounded noise. An analysis of convergence and stability is provided.

Keywords:Adaptive control, Stability of nonlinear systems Abstract: In this paper we consider the problem of steering a linear system to an unknown setpoint that is defined as the minimizer of an optimization problem. We give a gradient-based solution as well as a gradient-free approximation that, in the spirit of extremum seeking control, only requires measurements of the objective function. We further show that in both cases dynamic output feedback can be used if full state measurements are not available.

Keywords:Adaptive systems, Control of networks, Adaptive control Abstract: The synchronization of unknown systems is studied for both undirected and directed graphs. In the undirected setting it is shown that consensus can be achieved without an external consensus protocol (that is, without a high gain linear error input usually written as a function of the graph laplacian and the states in the network), but solely through local adaptive feedback. In the directed case several different scenarios are addressed. An emphasis is placed on analyzing the simplest possible control design to achieve the goal of consensus. This breaks from the pinning adaptive control literature where the most general case is usually addressed, inadvertently obscuring what is, and what is not needed to achieve stability. Also breaking from the literature in the area of Distributed Adaptive Control with Synchronization (DACS) we do not assume a-priori knowledge of a uniform bound on the plant state.

Keywords:Adaptive control, Identification for control, Stability of linear systems Abstract: In this paper, a new uncertainty identification method is introduced for both matched and unmatched uncertainties in an uncertain dynamical system. Online identifications of matched and unmatched uncertainties that can be linearly parameterized are ensured without requiring persistent excitation (PE) condition. Furthermore, constant weight matrix that parameterizes the unstructured uncertainties are guaranteed to stay bounded without PE. Findings are implemented on a hybrid adaptive control design, and global exponential stability is established.

Keywords:Adaptive systems, Distributed parameter systems, Estimation Abstract: We investigate systems stated as 2 x 2 hyperbolic partial differential equations (PDEs) affected at one boundary by a biased signal containing unknown sinusoids. We design an observer estimating the sinusoid's frequencies, bias, phases and amplitudes as well as the system states from sensing anti-collocated with the sinusoid. The theory is demonstrated in a simulation.

Keywords:Adaptive systems, Networked control systems, Adaptive control Abstract: Fundamental properties such as learning and consensus have been studied both in the adaptive control and network control literature. The use of an error feedback is essential for the realization of both properties. In adaptive control, error feedback is used to update adaptive parameters in an effort to accomplish learning and tracking. In network control, error feedback is used to achieve consensus. The two types of error feedback are seldom studied in concert. This paper takes a first step towards this objective and explores the implications of concomitantly achieving consensus and learning in adaptive and networked systems. Conditions under which synchronous inputs can enhance adaptation and learning are analyzed. The tradeoff between synchronization and learning is explored both in the context of two interacting dynamical systems and a network of dynamical systems interacting over a graph.

Keywords:Algebraic/geometric methods, Adaptive systems, Identification Abstract: Despite the many applications for subspace tracking, despite the renewed interest in e.g. distributed versions and despite the considerable literature on subspace tracking, some fundamental problems remain open. Here we give, for the first time, a global stability analysis of a noisy fixed gain subspace tracking algorithm in continuous time. Despite impressions given to the contrary in the literature we show the fixed gain algorithm does not converge but rather hovers in the vicinity of an associated averaged system.

Keywords:Hybrid systems, Constrained control, Robotics Abstract: This paper studies the problem of constructing in-block controllable (IBC) regions for affine systems. That is, we are concerned with constructing regions in the state space of affine systems such that all the states in the interior of the region are mutually accessible through the region's interior by applying uniformly bounded inputs. We first show that existing results for checking in-block controllability on given polytopic regions cannot be easily extended to address the question of constructing IBC regions. We then explore the geometry of the problem to provide a computationally efficient algorithm for constructing IBC regions. We also prove the soundness of the algorithm. Finally, we use the proposed algorithm to construct safe speed profiles for fully-actuated robots and for ground robots modeled as unicycles with acceleration limits.

Keywords:Hybrid systems, Discrete event systems, Automata Abstract: In this paper, we propose a novel controller design technique to track a reference trajectory for a class of hybrid systems having state-triggered jumps. The idea is, by gluing start and end points of jumps in the state space, to change the domain into another domain where the state jumps disappear. After gluing, the hybrid systems can be considered as continuous or piecewise continuous dynamical systems without any state jumps. Therefore, it would be possible to construct tracking controllers for the hybrid systems through conventional design methods. The proposed technique guarantees that the state converges to the reference except the region where jumps occur or arrive at. Simulation results for various examples illustrate the effectiveness of the proposed approach.

Keywords:Hybrid systems, Formal verification/synthesis, Model/Controller reduction Abstract: In this work, we develop a method for verifying Continuous-time Stochastic Hybrid Systems (CTSHSs) using the Mori-Zwanzig model reduction method, whose behaviors are specified by Metric Interval Temporal Logic (MITL) formulas. By partitioning the state space of the CTSHS and computing the optimal transition rates between partitions, we provide a procedure to both reduce a CTSHS to a Continuous-Time Markov Chain (CTMC), and the associated MITL formulas defined on the CTSHS to MITL specifications on the CTMC. We prove that an MITL formula on the CTSHS is true (or false) if the corresponding MITL formula on the CTMC is robustly true (or false) under certain perturbations. In addition, we propose a stochastic algorithm to complete the verification. Finally, as an example, we implement the method in a Billiard Problem.

Keywords:Hybrid systems, Stability of hybrid systems Abstract: There exist various methods for planning nominal trajectories to guide desired behaviours of non-linear systems, along with constructive methods for computing finite-time invariant sets, termed funnels, about locally-stabilized nominal trajectories. In order to achieve a desired behaviour defined by a set of nominal trajectories and their corresponding funnels, one has to switch from one local control to another at the right instances. This paper presents a general hybrid-control framework which is designed for correct switching between locally stabilizing controllers and can be used in conjunction with various approaches for funnel computation. Our framework prescribes exact connectivity conditions to be satisfied by the different funnels used such that the desired behaviour is achieved globally and in a robust manner. Due to its generality, the framework can be applied to implement a wide class of dynamic behaviours. An example of a periodic behaviour governed by our framework is provided.

Keywords:Hybrid systems, Switched systems, Algebraic/geometric methods Abstract: A causal modeling for an impulsive system with a state dependent switching surface is defined and analyzed on a new extended real space, denoted as Krylov hyperreals, which is based on the nonstandard analysis (NSA). The recent work of the authors contains the detailed construction of the extended space, and the generalized function on that space. In the first part of the paper, important concepts of NSA, and the suggested function space are reviewed. Next, a new generalization of a continuous but not differentiable function will be defined on the Krylov hyperreals in order to properly define a composition between singular and non differentiable function. By using an analogy to a spring and damper model, the authors suggest an equivalent causal model of the state dependent impulsive system by introducing the powers of singular control in the original continuous dynamics. A motivational example of a bouncing ball moving on a horizontal surface is analyzed to show the effectiveness.

Keywords:Hybrid systems, Vision-based control, Robust control Abstract: Recently developed neuromorphic vision sensors have become promising candidates for agile and autonomous robotic applications primarily due to, in particular, their high temporal resolution and low latency. Each pixel of this sensor independently fires an asynchronous stream of ``retinal events" once a change in the light field is detected. Existing computer vision algorithms can only process periodic frames and so a new class of algorithms needs to be developed that can efficiently process these events for control tasks. In this paper, we investigate the problem of textit{quadratically} stabilizing a continuous-time linear time invariant (LTI) system using measurements from a neuromorphic sensor. We present an H_infty controller that stabilizes a LTI system and provide the set of stabilizing DVS cameras for the given system. The effectiveness of our approach is illustrated on an unstable system.

Keywords:Nonlinear systems identification, Adaptive control, Control applications Abstract: The recognition of system parameters in uncertain complex dynamical networks with stochastic disturbance and time-varying delay is investigated in this note. By constructing a slave network and designing feedback controllers, the outer synchronization between two networks is achieved according to the Ithat{o} differential formula, LaSalle'e invariance principle. Meanwhile, the unknown system parameters in the uncertain complex networks and the control gains are obtained, respectively, based on the adaptive updating laws. Additionally, a numerical simulation is given to show the validity of the analytical results.

Keywords:Nonlinear systems identification, Estimation, Identification for control Abstract: The Wiener-Hammerstein model is a block-oriented model consisting of two linear blocks and a static nonlinearity in the middle. Several identification approaches for this model structure rely on the fact that the best linear approximation of the system is a consistent estimate of the two linear parts, under the hypothesis of Gaussian excitation. But, these approaches do not consider the presence of other disturbance sources than measurement noise. In this paper we consider the presence of a disturbance entering before the nonlinearity (process noise) and we show that, also in this case, the best linear approximation is a consistent estimate of underlying linear dynamics. Furthermore, we analyze the impact of the process noise on the nonlinearity estimation, showing that a standard prediction error method approach can lead to biased results.

Keywords:Nonlinear systems identification, Grey-box modeling, Numerical algorithms Abstract: This paper addresses maximum likelihood parameter estimation of continuous-time nonlinear systems with discrete-time measurements. We derive an efficient algorithm for the computation of the log-likelihood function and its gradient, which can be used in gradient-based optimization algorithms. This algorithm uses UD decomposition of symmetric matrices and the array algorithm for covariance update and gradient computation. We test our algorithm on the Lotka-Volterra equations. Compared to the maximum likelihood estimation based on finite difference gradient computation, we get a significant speedup without compromising the numerical accuracy.

Keywords:Nonlinear systems identification, Identification, Estimation Abstract: The objective of combined state and parameter estimation is to estimate both unmeasured states and unknown entries of the dynamics matrix. Since the dynamics involve products of states and parameters, this is a nonlinear estimation problem. The classical approach to this problem is to use the extended Kalman filter, although more recent techniques, such as the unscented Kalman filter, can be used. The goal of this paper is to determine conditions under which the combined state and parameter estimation problem is feasible. To do this, we recast this problem as an identifiability problem and, for several special cases, we develop necessary and sufficient conditions for identifiability, which provides necessary and sufficient conditions for feasibility of the combined state and parameter estimation problem.

Keywords:Nonlinear systems identification, Identification, Estimation Abstract: This paper introduces a simulation-based method for maximum likelihood estimation of stochastic Wiener systems. It is well known that the likelihood function of the observed outputs for the general class of stochastic Wiener systems is analytically intractable. However, when the distributions of the process disturbance and the measurement noise are available, the likelihood can be approximated by running a Monte-Carlo simulation on the model. We suggest the use of Laplace importance sampling techniques for the likelihood approximation. The algorithm is tested on a simple first order linear example which is excited only by the process disturbance. Furthermore, we demonstrate the algorithm on an FIR system with a cubic nonlinearity. The performance of the algorithm is compared to the maximum likelihood method and other recent techniques.

Keywords:Nonlinear systems identification, Identification Abstract: In this paper, the problem of variable selection is addressed for high-dimensional nonparametric additive nonlinear systems. The purpose of variable selection is to determine contributing additive functions and to remove non-contributing ones from the underlying nonlinear system. A two-step method is developed to conduct variable selection. The first step is concerned with estimating each additive function by virtue of kernel-based nonparametric approaches. The second step is to apply a nonnegative garrote estimator to identify which additive functions are nonzero in terms of the obtained nonparametric estimates of each function. The proposed variable selection method is workable without suffering from the curse of dimensionality, and it is able to find the correct variables with probability one under weak conditions as the sample size approaches infinity. The good performance of the proposed variable selection method is demonstrated by a numerical example.

Keywords:Networked control systems, Network analysis and control, Large-scale systems Abstract: In this paper, we show that dissipativity and passivity based control combined with event-triggered networked control systems (NCS) provide a powerful platform for designing cyber-physical systems (CPS). We propose QSR-dissipativity, passivity and finite-gain L2-stability conditions for an event-triggered NCS in cases where an input-output event-triggering sampler condition is located on the plant's output side, controller's output side, or both sides leading to a considerable decrease in communication load amongst sub-units in NCS. We show that the passivity and stability conditions depend on passivity levels for the plant and controller. Our results also illustrate the trade-off among passivity levels, stable performance, and system's dependence on the rate of communication between the plant and controller.

Keywords:Predictive control for linear systems, Stability of linear systems, Networked control systems Abstract: In this paper, we propose a new self-triggered formulation of Model Predictive Control for continuous time linear networked control systems. Our control approach, which aims at reducing the number of transmitting control samples to the plant, is derived by parallelly solving optimal control problems with different sampling time intervals. The controller then picks up one sampling pattern as a transmission decision, such that a reduction of communication load and the stability will be obtained. The proposed strategy is illustrated through comparative simulation examples.

Keywords:Discrete event systems, Communication networks, Switched systems Abstract: In this paper, we study optimal stationary sampling for transmission of measurements of a stochastic process from a source encoder to a source decoder through a costly communication channel. We measure information transferred over a time interval by the change in the decoder's entropy regarding the state of the process given the transmitted measurements. In our setting, the encoder employs a sampler to control the information flow in the channel. The problem is casted as a discounted infinite horizon optimization problem that takes into account the transferred information and the paid price. We derive the optimal stationary sampling policy, and propose two computational methods with convergence guarantees by using techniques from approximate dynamic programing. In addition, we introduce two triggering mechanisms based on the value of information and on the covariance threshold that can generate the optimal policy. Finally, we present some numerical and simulation results.

Keywords:Numerical algorithms, Optimization algorithms, Discrete event systems Abstract: In this paper, we propose a self-triggered algorithm to solve a class of convex optimization problems with time varying objective functions. It is known that the trajectory of the optimal solution can be asymptotically tracked by a continuous-time state update law. Unfortunately, implementing this requires continuous evaluation of the gradient and the inverse Hessian of the objective function which is not amenable to digital implementation. Alternatively, we draw inspiration from self-triggered control to propose a strategy that autonomously adapts the times at which it makes computations about the objective function, yielding a piece-wise affine state update law. The algorithm does so by predicting the temporal evolution of the gradient using known upper bounds on higher order derivatives of the objective function. Our proposed method guarantees convergence to arbitrarily small neighborhood of the optimal trajectory in finite time and without incurring Zeno behavior. We illustrate our framework with numerical simulations.

Keywords:Networked control systems, Estimation, Information theory and control Abstract: Event-based state estimation can achieve estimation quality comparable to traditional time-triggered methods, but with a significantly lower number of samples. In networked estimation problems, this reduction in sampling instants does, however, not necessarily translate into better usage of the shared communication resource. Because typical event-based approaches decide instantaneously whether communication is needed or not, free slots cannot be reallocated immediately, and hence remain unused. In this paper, novel predictive and self triggering protocols are proposed, which give the communication system time to adapt and reallocate freed resources. From a unified Bayesian decision framework, two schemes are developed: self-triggers that predict, at the current triggering instant, the next one; and predictive triggers that indicate, at every time step, whether communication will be needed at a given prediction horizon. The effectiveness of the proposed triggers in trading off estimation quality for communication reduction is compared in numerical simulations.

Keywords:Hybrid systems, Sampled-data control, Stability of nonlinear systems Abstract: This work is concerned with the exponential stability of an output-based control scheme where the measured output is subjected to event-triggered sampling. We propose a new event-based sampling criterion based on the memory of the measured output instead of only the current output. This allows to prevent accumulation of sampling times. The exponential stability is analyzed by using a Lyapunov-based approach, providing a link between the sampling criterion and the decay rate. Several numerical examples illustrate the effectiveness of the proposed event-triggered scheme.

Keywords:Distributed parameter systems, Lyapunov methods, Quantized systems Abstract: We consider a system of linear hyperbolic partial differential equations (PDEs) where the state at one of the boundary points is controlled using the measurements of another boundary point. For this system class, the problem of designing dynamic controllers for input-to-state stabilization in H^1-norm with respect to measurement errors is considered. The analysis is based on constructing a Lyapunov function for the closed-loop system which leads to controller synthesis and the conditions on system dynamics required for stability. As an application of this stability notion, the problem of quantized control for hyperbolic PDEs is considered where the measurements sent to the controller are communicated using a quantizer of finite length. The presence of quantizer yields practical stability only, and the ultimate bounds on the norm of the state trajectory are also derived.

Keywords:Distributed parameter systems Abstract: We solve the problem of stabilizing two coupled linear hyperbolic PDEs using actuation at both boundary of the spatial domain in minimum time. We design a novel Fredholm transformation similarly to backstepping approaches. This yields an explicit full-state feedback law that achieves the theoretical lower bound for convergence time to zero.

Keywords:Distributed parameter systems, Delay systems, Lyapunov methods Abstract: In this paper, we deal with the control of a transport PDE/nonlinear ODE cascade system in which the transport coefficient depends on the ODE state. We develop a PDE-based predictor-feedback boundary control law, which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed-loop system. The stability proof is based on an infinite-dimensional backstepping transformation that is introduced, with the aid of which, a Lyapunov functional is constructed. The relation of the PDE-ODE cascade to an ODE system with a state-dependent input delay, which is defined implicitly via an integral of the ODE state, is also highlighted and the corresponding equivalent predictor-feedback design is presented. The practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process.

Keywords:Control applications, Distributed parameter systems, Fluid flow systems Abstract: In this paper we consider the problems of modeling and control of counter-flow heat exchangers when one includes actuator dynamics as part of the model. Most models of heat exchangers assume zero axial conduction which is known to cause numerical problems and impacts control design. This paper extends earlier work where we now include full-flux terms and allow for actuator dynamics. Motivation for this paper comes from problems of design and control of vapor compression systems where the vapor compression cycle includes two heat exchangers, a compressor and an expansion valve. The control inputs to the condenser (heat exchanger one) are outputs of the the compressor and inputs to the evaporator (heat exchanger two) are outputs to the expansion valve. Thus, the dynamics of the compressor, motors and expansion valve are important when designing controllers for the heat exchangers. We focus on a simple heat exchanger model which includes actuator dynamics and use this model to evaluate the impact of including full-flux terms on controller design. We establish that as the axial conduction terms approach zero, one obtains convergence to the hyperbolic model with no axial conduction. In the case where the flux terms are dropped and the flow is zero, the resulting (degenerate) ODE control system is no longer stabailizble. Numerical examples are provided to illustrate the theoretical results.

Keywords:Distributed parameter systems, Stability of linear systems, Linear systems Abstract: This paper aims at illustrating how the control by interconnection methodology (energy-Casimir method) can be employed in the development of exponentially stabilising boundary control laws for a class of linear, distributed port-Hamiltonian systems with one dimensional spatial domain. The energy-Casimir method is the starting point to determine a state-feedback law able to shape the closed-loop Hamiltonian and achieve simple stability. Then, it is shown how to design a further control loop that guarantees exponential convergence. Thanks to this result, it is possible to overcome a limitation of standard damping injection strategies that, if combined with energy shaping control laws based on energy-balancing, are able to assure, in general, only asymptotic convergence. The methodology is illustrated with the help of a simple example, the boundary stabilisation of a lossless transmission line.

Keywords:Distributed parameter systems, Stability of nonlinear systems, Algebraic/geometric methods Abstract: Generalized monotone dilation in a Banach space is introduced. Classical theorems on existence and uniqueness of solutions of nonlinear evolution equations are revised. A universal homogeneous feedback control for a finite-time stabilization of linear evolution equation in a Hilbert space is designed using homogeneity concept. The design scheme is demonstrated for distributed finite-time control of heat and wave equations.

Keywords:Delay systems, Stability of linear systems, Lyapunov methods Abstract: A novel approach for carrying out the second step of the production of stability charts of neutral type time-delay systems is presented. It consists in detecting stability regions in the space of delays or other parameters, once the imaginary axis roots crossing boundaries have been found. It is based on recently reported stability tests in terms of the delay Lyapunov matrix which plays a central role in the framework of complete type Lyapunov-Krasovskii functionals. A number of improvements aiming at speeding up the computation of the delay Lyapunov matrix and the scan of the space of parameters are introduced. The method is tested on challenging academic examples of the literature, and its strength and limitations are discussed.

Keywords:Delay systems, Stability of linear systems Abstract: This paper presents a criterion of exponential stability for time-invariant linear delay systems of retarded type. The criterion, which is based on the delay Lyapunov matrix, generalizes the Lyapunov stability theorem for ordinary differential systems. We show how to construct a special matrix, which is positive definite, if the system is exponentially stable, and is not positive definite otherwise.

Keywords:Delay systems, Stability of linear systems Abstract: This paper proposes a systematic method to analyse the stability of systems with single delay with coefficient polynomial depending on the delay. Such systems often arise in, for example, life science and engineering systems. A method was presented by Beretta and Kuang in a 2002 paper. This paper extends their results to the general case with the exception of some degenerate cases. The interval of interest for the delay is partitioned to smaller intervals so that the magnitude condition generate a fixed number of frequencies as functions of the delay within each interval. The crossing conditions are expressed in a general form, and a simplified derivation for the first order derivative criterion is obtained.

Keywords:Delay systems, Stability of nonlinear systems, Lyapunov methods Abstract: We provide new asymptotically stabilizing backstepping controls for time-varying systems in a partially linear form. Instead of measuring the full current state, our main feedback design uses several time lagged values of a function of the state of the nonlinear subsystem, and has no distributed terms. Other advantages are that we do not require differentiability of the available nominal controls for the nonlinear subsystems, and that our controls do not contain Lie derivatives. This improves on a recent work in Automatica that covered the special case where the linear part has one integrator, since we now allow an arbitrary number of integrators.

Keywords:Stability of nonlinear systems, Delay systems, Lyapunov methods Abstract: Stability properties of monotone nonlinear systems with max-separable Lyapunov functions are considered in this paper, motivated by the following observations. First, recent results have shown that such Lyapunov functions are guaranteed to exist for asymptotically stable monotone systems on compact sets. Second, it is well-known that, for monotone linear systems, asymptotic stability implies the stronger properties of D-stability and robustness with respect to time-delays. This paper shows that similar properties hold for monotone nonlinear systems that admit max-separable Lyapunov functions. In particular, a notion of D-stability for monotone nonlinear systems and delay-independent stability will be discussed. The theoretical results are illustrated by means of examples.

Keywords:Delay systems, Stability of nonlinear systems, Time-varying systems Abstract: We provide a new sequential predictors approach for the exponential stabilization of linear time-varying systems with pointwise time-varying input delays. Our method circumvents the problem of constructing and estimating distributed terms in the stabilizing control laws, and allows arbitrarily large input delay bounds. We illustrate our method using a pendulum dynamics.

Keywords:Predictive control for nonlinear systems, Aerospace, Simulation Abstract: The paper considers a problem of integrated thrust and electrical power management for an aircraft. An advanced configuration of the aircraft electrical power system consisting of two generators driven by the gas turbine engine is considered. A Model Predictive Controller is designed to respond to thrust and electrical load commands while maintaining system operation at high efficiency setpoints and satisfying the input and state constraints, including surge margin limits. The design steps are described and closed-loop simulation results are reported based on the nonlinear system model.

Keywords:Predictive control for nonlinear systems, Chemical process control, Lyapunov methods Abstract: Managing production schedules and tracking time-varying demand of certain products while optimizing process economics are subjects of central importance in industrial applications. Various control methods have been developed to track and achieve a desired production schedule. Nevertheless, production schedule following is generally required for a small subset of the total process state vector. Therefore, there is a potential in many processes to accomplish the desired production schedule while maintaining economically optimal process operation. Motivated by this, the present work proposes an approach that targets achieving the desired production schedule while maximizing economics using economic model predictive control (EMPC), which is a feedback control approach that optimizes plant economics in a receding horizon fashion. Conditions for closed-loop stability are derived for a general class of nonlinear systems. The proposed EMPC scheme was applied to a chemical process example where the product concentration is requested to follow a certain production schedule. Simulation results demonstrate that the proposed EMPC was able to maintain closed-loop stability, achieve the desired production schedule, and maximize plant economics.

Keywords:Predictive control for nonlinear systems, Constrained control, Optimal control Abstract: This paper addresses the design of a suitable terminal set and terminal cost for discrete-time Economic Model Predictive Control schemes with convergence guarantees. Three design methods are proposed. The first two approaches rely on the existence of a (possibly nonlinear) auxiliary control law that stabilizes the origin of the error space defined by the distance to an economically optimal state-input trajectory pair. The first method exploits a given bound on the stage cost evaluated along the closed-loop system with the auxiliary control law. If such a bound is not available, but the auxiliary control law stabilizes the origin of the error space exponentially fast, then a second method is proposed. The last method addresses the case where the auxiliary control law is not available, but the linearization of the system around the desired economically optimal trajectory is stabilizable. Depending on the selection of the auxiliary law, the proposed method allows the design of closed-loop systems with a possibly global region of attraction even in the case of nonlinear constrained systems. An example is used to illustrate the properties of the proposed methods.

Keywords:Spacecraft control, Predictive control for nonlinear systems, Aerospace Abstract: This paper studies nonlinear model predictive control (MPC) for spacecraft attitude maneuver problems when continuous inputs with saturation by reaction wheels (RW) and quantized inputs by reaction control systems (RCS) are used. After providing optimization algorithm based on branch and bound methods, we derive linear matrix inequality (LMI) conditions to ensure the input-to-state stability (ISS) for RCS case and asymptotic stability (AS) for RW case. The results are evaluated for high-rate large angle attitude switching maneuver problems of an astronomical satellite.

Keywords:Predictive control for nonlinear systems Abstract: In this paper, we present two approaches for min-max economic model predictive control (MPC). The first is based on the standard approach for robust min-max stabilizing MPC which is well known from literature and transferred to the case of non-definite cost functions. The second is based on ideas from robust tube-based MPC. In contrast to an exact prediction of the error, invariant error sets are considered in the optimization. While this setup is in general more conservative, it can lead to optimization problems which are computationally more appealing. We provide a priori bounds on the asymptotic average performance for both approaches and discuss and compare them in detail.

Keywords:Predictive control for nonlinear systems, Linear parameter-varying systems Abstract: Nonlinear Model Predictive Control often suffers from excessive computational complexity, which becomes critical when fast plants are to be controlled. This papers presents an approach to NMPC that exploits the quasi-LPV framework. For quasi-LPV systems, the scheduling variables are determined by the state variables and/or inputs. By calculating an estimate of the state variables during prediction, the prediction model can be adapted to the estimated state evolution in each step. Stability of the proposed algorithm is enforced by the offline solution of an optimization problem with Linear Matrix Inequality (LMI) constraints. Furthermore, an iterative approach is presented with which the NMPC optimization problem can be handled by solving a series of Quadratic Programs (QP) or Second Order Cone Programs (SOCP) in each time step, which leads to computational efficiency. The algorithm is tested in simulation to highlight convergence of the prediction and stability of the closed-loop under contraints.

Keywords:LMIs, Adaptive control, Uncertain systems Abstract: Despite the similarities between polytopic uncertain systems and Takagi-Sugeno fuzzy models, there is a fundamental difference: the exact knowledge of the linear systems weighting functions (also known as membership functions in the fuzzy systems literature). This knowledge is usually incorporated into fuzzy control laws, which allows for less conservative controllers. This work proposes a novel set of LMI synthesis conditions which when feasible guarantees that an adaptive control law, mimicking a fuzzy control law, asymptotically stabilizes the uncertain polytopic system. A numerical example is presented to demonstrate the effectiveness of the proposed control law.

Keywords:LMIs, Constrained control, Computational methods Abstract: This paper presents the stability analysis of critically stable systems with slope-restricted nonlinearities, which are very common in many practical systems. The stability of such systems is guaranteed via combination of noncausal Zames-Falb and Popov IQC multipliers where the conditions are formulated in terms of convex LMI searches. Several numerical examples are presented where we show that, with only simple searches, the combination of the Popov and Zames-Falb IQCs significantly improves the results and reduces the computation burden.

Keywords:LMIs, Control applications, H-infinity control Abstract: An H_infty design for a dynamic pricing scheme in the smart grid is analyzed. The design uses fuzzy interpolation techniques and linear matrix inequality (LMI) approaches. Detailed construction of a fuzzy inference system used to produce price signals is provided. LMI conditions for dynamic pricing are derived using the Lyapunov theory. Numerical analysis of fuzzy gains in the pricing scheme is performed, exhibiting a less conservative design than a standard pricing scheme. Those analyses and derivations can facilitate further modifications when a different pricing scenario is encountered.

Keywords:Delay systems, LMIs, Stability of linear systems Abstract: It is well-known that the second-order systems that cannot be stabilized by a static output feedback without a damping term, may be stabilized by inserting an artificial time-delay in the feedback. The existing Lyapunov-based methods that may treat this case and that lead to stability conditions in terms of Linear Matrix Inequalities (LMIs) suffer from hight-dimensionality of the resulting LMIs possessing a large number of decision variables. In this paper we suggest simple Lyapunov functionals that lead to reduced-order LMIs with a small number of decision variables.

Keywords:Linear parameter-varying systems, LMIs, Optimization Abstract: This paper presents a novel approach to efficiently solve parameter-dependent (PD) linear matrix inequality (LMI) problems for, amongst others, linear parameter-varying (LPV) control design. Typically, stability and performance is guaranteed by finding a PD Lyapunov function such that a PD LMI is feasible on a parameter domain. To solve the resulting semi-infinite problems, we propose a novel LMI relaxation technique relying on B-spline basis functions. This technique provides less conservative solutions and/or a reduced numerical burden compared to existing approaches. Moreover, an elegant generalization of worst-case optimization to the optimization of any signal norm is obtained by expressing performance bounds as a function of the system parameters. This generalization yields better performance bounds in a large part of the parameter domain. Numerical comparisons with the current state-of-the-art demonstrate the generality and effectiveness of our approach.

Keywords:LMIs, Observers for nonlinear systems, Control applications Abstract: This paper develops a convex optimization method to analyze the feasibility of a nonconvex bilinear matrix inequality (BMI), which is traditionally treated as a NP hard problem. First, a sufficient condition for the convexity of a quadratic matrix inequality (QMI), which is a more general semidefinite constraint than a BMI, is presented. It will be shown that the satisfaction of sufficient convexity condition implies that the QMI constraint can be transferred into an equivalent linear matrix inequality (LMI) constraint, which can be efficiently solved by well-developed interior-point algorithms. This result constitutes perhaps the first systematic methodology to verify the convexity of QMIs in the literature of semi-definite programming (SDP) in Control. For the BMI problem, a method to derive a convex inner approximation is discussed. The BMI feasibility analysis method is then applied to a nonlinear observer design problem where the estimation error dynamics is transformed into a Lure system with a sector condition constructed from the element-wise bounds on the Jacobian matrix of the nonlinearities. The developed numerical algorithm is used to design a nonlinear observer that satisfies multiple performance criteria simultaneously.

Keywords:Power systems, Optimization Abstract: We study the problem of optimally placing energy storage devices in distribution networks to minimize total energy loss, focusing on structural results. We use a continuous linearized branch-flow model to model the distribution network. For the special case of a linear network, modeling a main feeder, we explicitly derive the optimal solution when all loads have the same shape and prove several useful monotonicity properties of the optimal solution. We illustrate through simulations that these structural properties hold approximately also on radial networks modeled by standard discrete nonlinear power flow models and even when loads have different shapes. We discuss how these structural results provide insight for the planning of energy storage devices.

Keywords:Power systems, Optimization algorithms, Smart grid Abstract: This paper is concerned with global optimization of an alternating current optimal power flow (ACOPF) problem for optimal design of power distribution systems. The global optimization is challenging due to the high nonconvexity and the large size of the problem. An enhanced decomposition-based global optimization method is developed, based on the optimization model and the global optimization framework presented by Frank and Rebennack (2015). The constraint qualification failure that may arise in the proposed optimization framework is avoided by a novel problem reformulation. Case study results demonstrate the potential of the proposed framework for global optimization of realistic ACOPF problems.

Keywords:Power systems, Power electronics, Control of networks Abstract: Ad hoc electrical networks are formed by connecting power sources and loads without pre-determining the network topology. These systems are well-suited to addressing the lack of electricity in rural areas because they can be assembled and modified by non-expert users without central oversight. There are two core aspects to ad hoc system design: 1) designing source and load units such that the microgrid formed from the arbitrary interconnection of many units is always stable and 2) developing control strategies to autonomously manage the microgrid (i.e., perform power dispatch and voltage regulation) in a decentralized manner and under large uncertainty. To address these challenges we apply a number of nonlinear control techniques---including Brayton-Moser potential theory and primal-dual dynamics---to obtain conditions under which an ad hoc dc microgrid will have a suitable and asymptotically stable equilibrium point. Further, we propose a new decentralized control scheme that coordinates many sources to achieve a specified power dispatch from each. A simulated comparison to previous research is included.

Keywords:Power systems, Reduced order modeling, Smart grid Abstract: In this paper, strong AC-grid connected VSC-HVDC systems are studied. Under specific conditions, such systems can suffer from both stability and poor damping related issues, which warrants a stability study. Analytical eigenvalue expressions can directly demonstrate the impact of physical or control parameters on the system stability. However, especially in case of high-order systems, such expressions are challenging to obtain. This paper suggests a method to symbolically represent approximative eigenvalues of two-terminal VSC-HVDC systems, which could also be used to analyze the system dynamics. In addition, by applying symbolic-isolation method, the order of a multi-terminal VSC-HVDC system can be reduced to an equivalent two-terminal VSC-HVDC system, which enables the proposed method to provide symbolic pole expressions. Numerical studies based on Matlab simulations are presented, showing the accuracy of the analytical eigenvalue expressions and providing useful hints on the impact of physical or control parameters.

Keywords:Power systems, Smart grid, Control of networks Abstract: Well known in the theory of traffic flows, Braess paradox states that in a congested network, it may happen that adding a new path between destinations can increase the level of congestion. In the case of transportation networks the phenomenon results from selfish decisions of network participants who seek to optimize their own performance metrics. Similar phenomena are now being studied in electric networks where an analogous increase in congestion can arise as a consequence of Kirchhoff's laws. This paper extends our recent results on Braess-like congestion phenomena in voltage controlled DC networks to the case of current controlled and mixed source networks. While the results below have qualitative characteristics that are similar to the voltage-controlled case, there appears to be more subtlety and even a degree of indeterminacy that point to the need for further research to understand the ways in which congestion in transmission and distribution networks will depend on changes in grid topologies.

Keywords:Power systems, Smart grid, Emerging control applications Abstract: We present a method for designing distributed generation and demand control schemes for secondary frequency regulation in power networks such that asymptotic stability and an economically optimal power allocation can be guaranteed. A dissipativity condition is imposed on net power supply variables to provide stability guarantees. Furthermore, economic optimality is achieved by explicit decentralized steady state conditions on the generation and controllable demand. We discuss how various classes of dynamics used in recent studies fit within our framework and give examples of higher order generation and controllable demand dynamics that can be included within our analysis. We also discuss how the dissipativity condition imposed can be easily verified for linear systems by solving an appropriate LMI. Our results are illustrated with simulations on the IEEE 68 bus system which demonstrate that the inclusion of controllable loads offer improved transient behavior and that an optimal power allocation among controllable loads is achieved.

Keywords:Hybrid systems, Spacecraft control, Stability of hybrid systems Abstract: The development of autonomous systems is a growing area of importance across a wide range of commercial, government, and civil applications. A number of new technical tools for the design and analysis of complex autonomous systems have been proposed in the literature, including the use of hybrid systems modeling and analysis. This paper develops an exemplar autonomous system problem, namely an autonomous spacecraft rendezvous, proximity operations, and docking (ARPOD) mission, as a benchmark problem for hybrid systems analysis and control techniques. The paper provides a complete mathematical description of the ARPOD hybrid dynamics/control problem, as well as providing details on variants that can be included to emphasize different elements of the hybrid system and to increase or decrease the complexity of the problem. Some baseline results are provided for comparison.

Keywords:Optimal control, Spacecraft control, Predictive control for linear systems Abstract: We investigate trajectory generation algorithms that allow a satellite to autonomously rendezvous and dock with a target satellite to perform maintenance tasks, or transport the target satellite to a new operational location. We propose a combination of path planning strategies for the different phases of rendezvous. In the first phase, the satellite navigates to a point in the Line of Sight (LOS) region of the target satellite. We show that the satellite's equations of motion are differentially flat in the relative coordinates, hence the rendezvous trajectory can be found efficiently in the flat output space without a need to integrate the full nonlinear dynamics. In the second phase, we use model predictive control (MPC) with linearized dynamics to navigate the spacecraft to the final docking location within a constrained approach envelope. We demonstrate feasibility of this study by simulating a sample docking mission.

Keywords:Hybrid systems, Optimization, Spacecraft control Abstract: We compute the reach-avoid set for space vehicle rendezvous and docking under continuous thrust. We model the space vehicle dynamics through the Clohessy-Wiltshire-Hill (CWH) equations, resulting in a switched hybrid system with affine, time-invariant dynamics. We exploit a closed-form solution to the CWH equations to analytically determine evolution of the boundary of the reach-avoid set, then modify the cost function of the reach-avoid variational equations to identify minimum thrust trajectories. Our contribution is two-fold: 1) the set of states from which there exists a maneuver (irrespective of the cost) that will allow a spacecraft to reach a target while remaining within a line-of-sight cone, and 2) a minimum-thrust cost that allows quick assessment, for points that lie within the reach-avoid set, of minimum fuel trajectories.

Keywords:Autonomous systems, Uncertain systems, Spacecraft control Abstract: As the complexity of the specifications that must be met by a system increases, hierarchical control protocols that merge control and planning decisions at multiple levels of abstraction become necessary. For such hierarchical reasoning, a suitable finite-state abstraction for dynamical systems evolving over continuous state spaces may be needed. The implementation of existing controllers derived using a finite-state abstraction often require that the current continuous state be known exactly, in order to guarantee that the required transitions in the finite-state abstraction occur. When the measurements are partial or noisy, the true state is unknown, and these controllers cannot be implemented. We propose an abstraction that can be used to overcome the uncertainty in the state resulting from imperfect measurement, at the cost of providing only probabilistic guarantees. The abstraction is based on the filter used to maintain an estimate of the true state. We show how the abstraction can be used to create a time-varying policy which maximizes the minimum probability that a target discrete state is reached in finite time from any initial state.

Keywords:Supervisory control, Spacecraft control, Hybrid systems Abstract: We consider the problem of rendezvous, proximity operations, and docking of an autonomous spacecraft. The problem can be conveniently divided into four phases: 1) rendezvous with angles-only measurements; 2) rendezvous with range measurements; 3) docking phase; and 4) docked phase. Due to the different constraints, available measurements, and tasks to perform on each phase, we study this problem using a hybrid systems approach, in which the system has different modes of operation for which a suitable controller is to be designed. Following this approach, we characterize the family of individual controllers and the required properties they should induce to the closed-loop system to solve the problem within each phase of operation. Furthermore, we propose a supervisor that robustly coordinates the individual controllers so as to provide a solution to the problem. Due to the stringent mission requirements, the solution requires hybrid controllers that induce convergence, invariance,or asymptotic stability properties, which can be designed using recent techniques in the literature of hybrid systems. In addition, we outline specific controller designs that appropriately solve the control problems for individual phases and validate them numerically.

Keywords:Aerospace, Hybrid systems, Algebraic/geometric methods Abstract: This paper presents tracking control systems on the two-sphere, that is composed of unit-vectors in the three dimensional Euclidean space. First, a smooth feedback control system is constructed to follow a desired trajectory on the two-sphere, while guaranteeing almost global exponential stability. Next, a hybrid control scheme is proposed to achieve global exponential stability by introducing an additional expelling mode. It is shown that there is one dimensional degree of freedom in the expelling mode, and it is optimized to minimize selected measures of the overall tracking performance. The proposed optimal construction of hybrid controls, while guaranteeing global attractivity on the two-sphere is the unique contribution of this paper. These are illustrated by numerical examples.

Keywords:Genetic regulatory systems, Cellular dynamics, Biotechnology Abstract: Living organisms employ endogenous negative feedback loops to maintain homeostasis despite environmental fluctuations. An intriguing challenge in Synthetic Biology is that of designing and implementing synthetic circuits to control host cells' behavior, thus mimicking what natural evolution has refined and conserved. The high degree of circuit complexity required to accomplish this task, and the intrinsic modularity of classical control schemes, suggest the implementation of synthetic endogenous feedback loops across more than one cell population. The distribution of the sensing, computation and actuation functions required to achieve regulation, to different cell populations within a consortium allows to reduce the genetic engineering in a particular cell and to increase the robustness as well as the possibility of reusing the synthesized circuits. Here we propose and study, in-silico, the design of a synthetic microbial consortium implementing a feedback controller across two cell populations.

Keywords:Genetic regulatory systems, Modeling, Cellular dynamics Abstract: Real-time automatic regulation of gene expression in living cells is a key technology for synthetic biology. Unlike traditional control engineering applications, cells grow and divide over time, and the natural variability arising in individual cell gene expression makes the population time-varying and heterogeneous. Therefore, the application of tried and tested control approaches can be often problematic. Here, using a microfluidics-based experimental platform, in which either glucose or galactose is provided to the cells, we measured expression from the galactose-inducible promoter in individual cells for thousands of minutes. We identified single cell linear dynamical models across hundreds of cells via a recently proposed linear mixed-effects identification strategy. We show that these models are able to capture the expression dynamics of single cells but also the mean and variance of the population, thus making realistic simulation of gene expression possible. We then compared the performance of a Model-Predictive-Control strategy to solve regulation and tracking problem when based either on a deterministic model of the mean expression of the cell population, or on the individual models of the single cells.

Keywords:Biological systems, Genetic regulatory systems, Systems biology Abstract: The characterization of biological networks via mathematical models often involves cycles of experimental perturbations and measurements, followed by the use of a network inference method. Here we study an engineered genetic circuit, introduced in a recent paper by the authors, and report additional analysis and interpretation. Using this synthetic network as a benchmark, we find that the application of the modular response analysis (MRA) network inference method leads to the discovery of a hidden, nontrivial ghost regulatory edge, which was not explicitly engineered into the network. Importantly, this result is not evident from direct inspection of the experimental measurements and global response coefficients. To probe the global to local conversion in MRA, we use conditionally randomized global response matrices to obtain distributions of local response coefficients and demonstrate that sign changes are numerically possible. Additionally, using simulations of a cascade network in a biochemical setting which does not take into account resource limitations, we show that MRA cannot return ghost edges, which points to the impact of the cellular milieu and in particular the use of shared resources. Taking resource availability into account during reverse engineering may allow for closer approximation of the cellular environment and points to a potential opportunity for network characterization strategies.

Keywords:Biomolecular systems, Systems biology, Cellular dynamics Abstract: Intracellular transport of cargoes inside eukaryotic cells is primarily carried out by bio-mechanical machines called molecular motors. These motors facilitate the directed transfer of intracellular cargo to desired locations inside the cell. In vivo modes of transport often involve multiple agents, possibly of different types, teaming up to carry a common cargo. We analyze the stochastic dynamics of such cargos and prove that the probability distribution of various motor-motor configurations in an ensemble reaches a unique steady state. Existence of such a unique steady state indicates a degree of robustness of the system of multiple motors sharing a cargo. Analysis of the steady state distribution for an ensemble of two kinesin motors for varying load forces reveals a degree of cooperativity between the motors, where configurations that have the two motors clustered together are favored for moderate loads. We further show that when subjected to high forces, such as those encountered due to obstacles along the path of travel, motors preferably adopt a configuration that facilitates high probability of regaining motion once the obstacle is removed. Simulation results of the steady state distribution of a two motor ensemble for low, moderate and high load forces are presented, which corroborate analytical studies.

Keywords:Biomolecular systems, Biological systems, Grey-box modeling Abstract: Without accounting for the limited availability of shared cellular resources, the standard model of gene expression fails to reliably predict experimental data obtained in vitro. To overcome this limitation, we develop a dynamical model of gene expression explicitly modeling competition for scarce resources. In addition to accurately describing the experimental data, this model only depends on a handful of easily identifiable parameters with clear physical interpretation. Based on this model, we then characterize the combinations of protein concentrations that are simultaneously realizable with shared resources. As application examples, we demonstrate how the results can be used to explain similarities/differences among different in vitro extracts, furthermore, we illustrate that accounting for resource usage is essential in circuit design considering the toggle switch.

Keywords:Biomolecular systems, Systems biology, Genetic regulatory systems Abstract: We examine the capacity of artificial biomolecular networks to respond to perturbations with structurally signed steady-state changes. We consider network architectures designed to balance their output production as a function of downstream demand: the species producing the output, called a source, up- or down-regulates its production rate as a function of the demand. Using an exact algorithm we show that, in certain negative feedback architectures, changes in the total source concentration cause structurally signed variations of the steady-state output concentration, regardless of reaction rate parameters. Conversely, positive feedback schemes can exhibit the same signed behaviour for reasonable (but not for arbitrary) values of the parameters. Numerical simulations demonstrate how the steady-state concentrations of different network architectures vary, responding to perturbations in total source amounts, consistently with our structural previsions.

Keywords:Robust adaptive control, Optimal control, Neural networks Abstract: This paper presents a complete answer to the longstanding unanswered question of what value iteration (VI) is for continuous-time, continuous-state-action space nonlinear systems. Based on this proposed VI, we develop a new data-driven adaptive optimal control methodology for unknown nonlinear systems. As compared with the existing literature of adaptive dynamic programming (ADP) for continuous-time systems which often uses policy iteration (PI), an initial admissible control policy is no longer required. By means of the obtained result, a non-model-based adaptive optimal control design is given. The effectiveness of the proposed methodology is also illustrated by an example.

Keywords:Biologically-inspired methods, Neural networks, Adaptive control Abstract: The ﬂapping microrobot known as RoboBee is the ﬁrst robot to demonstrate insect-scale ﬂight, as well as the most capable ﬂying robotic insect to date. Controlled hover, trajectory-following, and perching have been accomplished by means of onboard sensors and actuators fabricated with the robot using a “pop-up book MEMS” process based on smart composite microstructures. This paper presents a RoboBee bio-inspired controller that closes the loop between the onboard sensors and actuators by means of a leaky integrate-and-ﬁre spiking neural network that adapts in ﬂight using a reward-modulated Hebbian plasticity mechanism.

Keywords:Direct adaptive control, Neural networks, Uncertain systems Abstract: This paper presents a new study on adaptive control of non-nanonical discrete-time neural network systems which do not have explicit relative degrees and cannot be directly dealt with by using feedback linearization control.The paper derives new results for the relative degrees of such systems using the implicit function theory to solve the issue of implicit dependence on system input in the process of feedback linearization. Such implicit input dependence is typically caused by time-advance operation for discrete-time systems, different from their continunous-time counterparts under time-differentiation operation leading to explicit input dependence. New relative degree formulations are employed to achieve desired system reparametrization for adaptive control.It develops an adaptive control scheme with analysis for relative degree one systems and an adaptive control design for relative degree two systems with simulation results to show desired system performance and discussion on some technical issues.

Keywords:Neural networks, Direct adaptive control, Lyapunov methods Abstract: Abstract--- In this paper, neural networks (NNs) are utilized in the backstepping approach to design a control input by approximating unknown dynamics of the strict-feedback nonlinear system with event-sampled inputs. The system state vector is assumed to be measurable. As part of the controller design, first, local input-to-state-like stability (ISS) for a continuously sampled controller that has been injected with bounded measurement errors is demonstrated and, subsequently, an event-execution control law is derived such that the measurement errors are guaranteed to remain bounded. Lyapunov theory is used to demonstrate that the tracking errors and the NN weight estimation errors for each NN are locally uniformly ultimately bounded (UUB) in the presence bounded disturbances, NN reconstruction errors, as well as errors introduced by event-sampling. Simulation results are provided to illustrate the effectiveness of the proposed controller.

Keywords:Neural networks, Robust control, Predictive control for nonlinear systems Abstract: The paper deals with determining the neural network model uncertainty for the purpose of robust controller design. The approach presented in the paper is based on the application of optimum experimental design for the choice of sequences providing the most informative data during the training of neural network. As a criterion quantifying the quality of training process a measure operating on the Fisher Information Matrix related to the estimates of network parameters is used. Then, it is possible to analyze the variance of the predicted network response and estimate how possible variations of parameter values influence the changes observed in the predicted model output. This allows to construct an appropriate cost function for the control system taking into account the model uncertainty and incorporate it into model predictive control scheme.

Keywords: Abstract: In formal verification, the goal is to check whether the executions of a system satisfy a rich property, usually expressed as a temporal logic formula. While the formal verification problem received a lot of attention from the formal methods community for the past thirty years, the dual problem of formal synthesis, in which the goal is to synthesize or control a system from a temporal logic specification, has not received much attention until recently. This tutorial paper provides a self-contained exposition on formal synthesis of control strategies for a particular class of dynamical systems. Central to this paper is the concept of transition system, which is shown to be general enough to model a wide variety of dynamical systems. It is shown how abstractions can be constructed by using simulation and bisimulation relations. The control specifications are restricted to formulas of Linear Temporal Logic (LTL) and some fragments of LTL, which are introduced together with the corresponding automata and the automata games used to generate control strategies for finite transition systems. At the end, we show how such control strategies can be adapted to discrete-time piecewise affine systems. Several examples are provided throughout the paper.

Keywords:Networked control systems, Control system architecture, Stability of nonlinear systems Abstract: In this paper, we propose a systematic method to design retrofit controllers for networked nonlinear systems. The retrofit controller, which consists of a linear state feedback controller and a dynamical compensator, can improve the control performance for a subsystem of interest, while guaranteeing the stability of the whole closed-loop system. Towards the retrofit controller design, we introduce a type of state-space expansion, called hierarchical expansion. The cascade structure of the hierarchical expansion realization enables the systematic design of stabilizing controller for a low-dimensional linear model extracted from the subsystem of interest. As a result, we can design a retrofit controller without explicit consideration of the dynamics of subsystems other than the subsystem of interest.The effectiveness of the proposed method is demonstrated through a power network example.

Keywords:Networked control systems, Agents-based systems, Cooperative control Abstract: The present paper investigates the robustness of the consensus protocol over weighted directed graphs using the Nyquist criterion. The limit to which a single weight can vary, while consensus among the agents can be achieved, is explicitly derived. It is shown that even with a negative weight on one of the edges, consensus may be achieved. The result obtained in this paper is applied to a directed acyclic graph and to the directed cycle graph. Graph theoretic interpretations of the limits are provided for the two cases. Simulations support the theoretical results.

Keywords:Networked control systems, Agents-based systems, Network analysis and control Abstract: This paper develops a novel distributed event-triggered algorithm for achieving multi-agent consensus while guaranteeing a fully Zeno-free triggering for emph{all} the agents. In this framework, the controller input and event detector are based on local measurements in terms of relative states with respect to neighboring agents, and each agent updates its control input only at its own triggering instants. A bounded and convergent function is included in the event detector function for each agent, which avoids the comparison of event error term to a zero threshold in the zero-crossing scenario. We also revisit several popular event-triggered consensus algorithms reported in the literature, clarify some issues relating to Zeno triggering, consensus convergence, communication/measurement requirements, local/global coordinate frames, etc., and highlight the advantages of the event-triggered consensus algorithm proposed in this paper.

Keywords:Networked control systems, Control system architecture, Modeling Abstract: This paper presents the formulation, modelling and design of a fixed structure topology for potential application in wireless networked control systems. The topology consists of a standard plant system, an output feedback controller system, and intermediate transfer and receiving network systems. The paper defines the topology and addresses the modelling of the closed-loop control system. It presents a modelling framework to design the controller, the transfer network, and the receiving network systems. Also, the paper discusses a design procedure of using shared network systems for a closed-loop control system with multiple plant and controller systems. The design procedures utilize LMI-based algorithms and deliver an internally stable closed-loop control system whose inputs and outputs satisfy an ell_2 - ell_{infty} performance criterion. The practicality of the design procedures is demonstrated using an illustrative example.

Keywords:Networked control systems, Adaptive control, Distributed control Abstract: Networked Distributed Control Systems (NDCS) consist of a number of interacting subsystems and usually face the challenge of delays induced by the communication network. In this paper we consider the case where each subsystem communicates with other subsystems its state information with a communication delay. We assume that each subsystem knows its own dynamics but does not know how neighboring subsystems affect its dynamics, i.e., the interconnection matrices are unknown. We proposed local robust adaptive control schemes whose objective is to stabilize the local subsystems, weaken the interconnections and guarantee global stability for the NDCS despite the communication delays. We showed analytically that if the unknown interconnections can be weakened by each subsystem and if the communication delay is small the overall system is exponentially stable.

Keywords:Networked control systems, Cooperative control, Autonomous robots Abstract: In this paper, we discuss a general problem of formation feasibility for multi-agent coordination control when individual agents have kinematics constraints modelled by affine nonlinear control systems with possible drift terms. All agents need to work cooperatively to maintain a global formation task described by edge constraints. For such multi-agent group, we assume that different agents may have totally different dynamics, which brings the problem of coordination control of networked heterogeneous systems. Based on concepts of (affine) distribution and codistribution, we propose a unified framework and an algebraic condition to determine the existence of feasible motions under both kinematic constraints and formation constraints. In the case that feasible motions exist, we propose a systematic procedure to obtain an equivalent dynamical system which generates all types of feasible motions. Examples involving coordination control of constant-speed agents are provided to demonstrate the application of this coordination control framework.

Keywords:Agents-based systems, Variable-structure/sliding-mode control, Networked control systems Abstract: Most of the existing results on anti-disturbance consensus control of multi-agent systems focus on matched- disturbance rejection and the disturbances are assumed to be constant or slowly time-varying. This paper investigates the consensus control problem of double-integrator multi- agent systems with mismatched disturbances, which can be some kinds of faster time-varying disturbances, such as ramp and higher-order disturbances. To estimate the higher-order disturbances and their derivatives, for each agent, a gener- alized proportional integral observer (GPIO) is constructed. By distributedly employing the disturbances estimates, a kind of nonlinear sliding-mode surfaces are developed for both leaderless and leader-follower multi-agent systems. Based on the proposed surfaces and the disturbances estimates, com- posite consensus protocols are designed for both cases, which guarantee the global asymptotical stability of the consensus error systems. Simulation results show the effectiveness of the proposed algorithms.

Keywords:Agents-based systems Abstract: We consider the problem of finding exact statistical characterizations of the Bernoulli trials network size estimator, a simple algorithm for distributedly counting the number of agents in an anonymous communication network for which the probability of committing estimation errors scales down exponentially with the amount of information exchanged by the agents. The estimator works by cascading a local, randomized, voting step (i.e., the i.i.d. generation of some Bernoulli trials) with an average consensus on these votes. We derive a tight upper bound on the probability that this strategy leads to an incorrect estimate, and refine the offline procedure for selecting the Bernoulli trials success rate.

Keywords:Agents-based systems Abstract: This paper studies the rigid formation control problem of multi-agent systems, for which finding a local interaction law ensuring global convergence towards a desired formation is the main challenge. A sliding mode control law is proposed in this paper, which can steer all the agents to a desired rigid formation in any dimensional space for arbitrarily initial configuration. The main idea is to firstly make the trajectories of all the agents reach a sliding surface in finite time and secondly govern the agents towards the desired rigid formation while confining the motion in the sliding surface. Thus, the difficulty in achieving global convergence towards a desired formation is reduced to a much lower dimensional state space with much less number of agents being controlled to satisfy inter-agent distance constraints. Simulation results are provided to illustrate the effectiveness of our proposed control schemes.

Keywords:Cooperative control, Agents-based systems, Spacecraft control Abstract: This paper provides a novel analysis of the global convergence properties of a well-known consensus protocol for multi-agent systems that evolve in continuous time on the n-sphere. The feedback is intrinsic to the n-sphere, i.e. it does not rely on the use of local coordinates obtained through a parametrization. It is shown that, for any connected undirected graph topology and all natural numbers except 1, the consensus protocol yields convergence that is akin to almost global consensus in a weak sense. Simulation results suggest that actual almost global consensus holds. This result is of interest in the context of consensus on Riemannian manifolds since it differs from what is known with regard to the 1-sphere and SO(3) where more advanced intrinsic consensus protocols are required in order to generate equivalent results.

Keywords:Cooperative control, Agents-based systems Abstract: This paper studies the formation control problem of a leader-follower heterogeneous network, for which some agents can freely fly in a 3D space while some others are confined in a 2D space. The sensing graph is assumed to be directed and the onboard local coordinate systems associated with the agents may not be coincident with each other. More specifically, the agents may have aligned z-axis but hold inconsistent x and y axes due to the absence of a common sense about north. This paper develops a distributed formation control law that solves the formation control problem for a leader-follower heterogeneous network without relying on a common coordinate system. Moreover, it is shown that the proposed control law also guarantees global convergence towards any desired formation shape as long as certain graph connectivity conditions hold. Simulation results are also provided to validate our control strategy.

Keywords:Agents-based systems, Stability of nonlinear systems Abstract: In this paper, we focus on one of the motion coordination problems called attitude synchronization. We propose a continuous-time protocol to align the states of a network of agents evolving in the space of rotations SO(3). Our work is related to the Riemannian consensus , which is a general extension of classical consensus algorithms to Riemannian manifolds. Nevertheless, the existing algorithms have the problem of either lack of global convergence or slow convergence rate. We show how to modify them so that the states of the agents can be aligned from almost any initial condition and also in faster convergence speed.

Keywords:Cooperative control, Networked control systems, Randomized algorithms Abstract: We investigate resilient consensus in a network of integer-valued agents in the presence of malicious agents. The goal of the healthy, normal agents is to form consensus in their state values, which may be disturbed by the non-normal, malicious agents. In this paper, we study update rules of the agents having asynchrony in the update times and also inter-agent communications with non-uniform, time varying, and bounded time delays. Using a simple mean subsequence reduced (MSR) algorithm for ignoring the extreme values affecting each normal agent, we solve the resilient quantized consensus problem in the presence of totally/locally bounded adversarial agents. We employ randomization both in quantization and update times. The results are examined through a numerical example.

Keywords:Cooperative control, Optimization algorithms, Agents-based systems Abstract: This paper addresses the persistent coverage problem, in which a group of autonomous robots must visit periodically a finite set of interest points and spend some time covering them, which we call coverage time. An optimization problem to calculate the optimal coverage times is formulated, and sufficient conditions for the existence of solution are given. In particular, a linear cost function is considered to solve the problem as a linear program. An iterative algorithm, which runs on the solution, is proposed to reduce the lengths of the predefined paths traveled by the robots in a finite number of iterations while maintaining optimal coverage times. Moreover, path planning is included in the optimization problem, computing specific weights in the cost function, and thus reducing the traveled distances and the total time spent covering. Simulation results demonstrate the performance of the approach.

Keywords:Cooperative control, Sensor networks, Estimation Abstract: In this paper, we address the problem of controlling a network of mobile sensors to estimate a collection of hidden states to a user-specified accuracy. The mobile sensors simultaneously take measurements of the hidden states, fuse them in a distributed filter, and plan their next views in order to minimize expected uncertainty. This formulation leads to an optimization problem with as many coupled LMI constraints as the number of hidden states. The network solves this problem by means of a new distributed random approximate projections method that is robust to the state disagreement errors that will exist among the robots as the distributed filter fuses the collected measurements and is computationally light enough to handle large numbers of hidden states.

Keywords:Spacecraft control, Cooperative control, Networked control systems Abstract: In this paper, we consider two problems dealing with the partial attitude synchronization of a multi-satellite system in which the satellites, modeled as rigid bodies, are underactuated. Having control authority about only two of the three principal axes, the objective is to align the uncontrolled third axis of all satellites such that they point along the same direction. Two control laws are proposed, one which aligns two satellites towards the same direction in inertial space, and another one which synchronizes an N-satellite system such that the satellites align their underactuated axes towards a fixed inertial direction. The synchronization discrepancy between the satellites is expressed in a unique parameterization that describes the uncontrolled axis of one satellite in the frame of the other via a stereographic projection, while the velocity discrepancy is described using a partial angular velocity difference.

Keywords:Cooperative control, Switched systems, Spacecraft control Abstract: In this paper, we study attitude synchronization for elements in the unit sphere of R3 and for elements in the 3D rotation group, for a network with switching topology. The agents' angular velocities are assumed to be the control inputs, and a switching control law for each agent is devised that guarantees synchronization, provided that all elements are initially contained in a given region, unknown to the network. The control law is continuous on the state of the system, and therefore global convergence to a synchronized network cannot be attained. The control law is decentralized and it does not require a common orientation frame among all agents. We refer to synchronization of unit vectors in R3 as incomplete synchronization, and of 3D rotation matrices as complete synchronization. Our main contribution lies on showing that these two problems can be analyzed under a common framework, where all elements' dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension.

Keywords:Cooperative control Abstract: This paper aims at solving the sign-consensus problem of linear multi-agents system, i.e., the signs of all agents’ states achieve consensus. The communication network is modeled by a signed directed graph, where both cooperative and competitive interactions coexist among the agents. Each individual agent is assumed to access only the local information, and a fully distributed control protocol is proposed. Using this control protocol, we find that sign consensus can be achieved without requiring the graph to have an eventually positive adjacency matrix.

Keywords:Distributed control, Agents-based systems, Networked control systems Abstract: We introduce new insights into the network centrality based not only on the network topology but also on the network dynamics. The focus of this paper is on the class of uncertain linear consensus networks in continuous time, where the network uncertainty is modeled by structured additive Gaussian white noise input on the update dynamics of each agent. The performance of the network is measured by the expected dispersion of its states in steady-state. This measure is equal to the square of the H_2 norm of the network, and it quantifies the extent by which its state is away from the consensus state in steady-state. We show that this performance measure can be explicitly expressed as a function of the Laplacian matrix of the network and the covariance matrix of the noise input. We investigate several structures for the noise input and provide engineering insights on how each uncertainty structure can be relevant in real-world settings. Then, a new centrality index is defined to assess the influence of each agent or link on the network performance. For each noise structure, the value of the centrality index is calculated explicitly, and it is shown that how it depends on the network topology as well as the noise structure. Our results assert that agents or links can be ranked according to this centrality index and their rank can drastically change from the lowest to the highest, or vice versa, depending on the noise structure.

Keywords:Agents-based systems, Autonomous robots, Robotics Abstract: The increased diffusion of service robots operating in tight collaboration with humans has renewed the interest of the scientific community towards realistic human motion models. In this paper, we present the Headed Social Force Model, a modeling approach enriching Helbing's Social Force Model with Laumond's human locomotion models. The proposed solution is shown to inherit the best features of either models, being able to reliably reproduce pedestrians' motions both in free space and in highly crowded environments. Extensive numerical simulations are presented in order to evaluate the performance under very different operating conditions.

Keywords:Agents-based systems, Network analysis and control, Learning Abstract: This paper proposes models of learning process in groups of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science.

Keywords:Network analysis and control Abstract: The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2^{n}-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is "fast-mixing" when the LTI system is stable, i.e. when β/δ < 1/λ_{max}(A) (where β is the infection rate per link, δ is the recovery rate, and λ_{max}(A) is the largest eigenvalue of the network's adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.

Keywords:Game theory, Network analysis and control Abstract: We study the perfect Bayesian equilibria of a leader follower game of incomplete information. The follower makes a noisy observation of the leader’s action (who moves first) and chooses an action minimizing her expected deviation from the leader's action. Knowing this, leader who observes the realization of the state, chooses an action that minimizes her distance to the state of the world and the ex-ante expected deviation from the follower's action. We show the existence of what we call "near piecewise-linear equilibria" when there is strong complementarity between the leader and the follower and the precision of the prior is poor. As a major consequence of this result, we prove local optimality of a class of slopey quantization strategies which had been suspected of being the optimal solution in the past, based on numerical evidence for Witsenhausen's counterexample.

Keywords:Agents-based systems, Network analysis and control, Cooperative control Abstract: The discrete-time Altafini model is an opinion dynamics model in which the interactions among a group of agents are described by a time-varying signed digraph. This paper first uses graph theoretic constructions to study modified versions of the Altafini model in which there are communication delays or quantized communication. The condition under which consensus in absolute value or bipartite consensus is achieved proves to be the same as the condition in the delay-free case. The paper also analyzes the performance of the model where the information exchanged between neighboring agents is subject to a certain type of deterministic uniform quantization. We show that in finite time and depending on initial conditions, the model on any static, connected, undirected signed graph will either cause all agents to reach a quantized consensus in absolute value, or will lead all variables to oscillate in a small neighborhood around the absolute value.

Keywords:Mean field games, Stochastic optimal control, Decentralized control Abstract: We consider a class of discrete-time stochastic Stackelberg dynamic games with one leader and the N followers where N is sufficiently large. The leader and the followers are coupled through a mean field term, representing the average behavior of the followers. We characterize a Nash equilibrium at the followers level, and a Stackelberg equilibrium between the leader and the followers group. To circumvent the difficulty that arises in characterizing a Stackelberg-Nash solution due to the presence of a large number of followers, our approach is to imbed the original game in a class of mean-field stochastic dynamic games, where each follower solves a generic stochastic control problem with an approximated mean-field behavior and with an arbitrary control for the leader. We first show that this solution constitutes an epsilon-Nash equilibrium for the followers, where epsilon can be picked arbitrarily close to zero when N is large. We then turn to the leader's problem, and show that the associated local optimal control problem, constructed via the mean field approximation, admits an (epsilon_1,epsilon_2)-Stackelberg equilibrium, where both epsilon_1 and epsilon_2 are arbitrarily close to zero as N becomes arbitrarily large. Numerical examples included in the paper illustrate the theoretical results.

Keywords:Game theory, Mean field games, Hierarchical control Abstract: aper studies the connections between mean-field games and the social welfare optimization problems. We consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean field term that depends on the mean of the population states. We show that under some mild conditions any epsilon-Nash equilibrium of the mean field game coincides with the optimal solution to a convex social welfare optimization problem. The results are proved based on a general formulation in the functional spaces and can be applied to a variety of mean field games studied in the literature. Our result also implies that the computation of the mean field equilibrium can be cast as a convex optimization problem, which can efficiently solved by a decentralized primal dual algorithm.

Keywords:Game theory, Optimization algorithms, Variational methods Abstract: We consider a subclass of N-player stochastic Nash games in which each player solves a parametrized stochastic optimization problem. In deterministic regimes, best response schemes have been shown to be convergent under a suitable spectral property associated with the proximal-response map. However, a direct application of this scheme to stochastic settings requires obtaining exact solutions to stochastic optimization problems at every step. Instead, we propose an {em inexact} generalization of this scheme in which an inexact solution to the best response problem is computed where the player-specific inexactness sequence is assumed to be separable. Notably, this scheme is an implementable single-loop scheme that requires a fixed (but increasing) number of stochastic gradient steps to compute an inexact solution to the best response problem. On the basis of this framework, we make several contributions: (i) The presented inexact best-response scheme produces iterates that converge to the unique equilibrium in mean; (ii) Surprisingly, we show that the iterates converge at a prescribed {em linear} rate with a prescribed constant rather than a sub-linear rate; and (iii) Finally, by assuming that an inexact solution is computed by a stochastic approximation scheme, the overall iteration complexity for computing an epsilon-Nash equilibrium less that {cal O}(yx {sqrt{N}} /epsilon)^{2+us{delta}} where us{delta} is a positive scalar. Additionally, we show that the upper bound of this effort is shown to be Omega(yx{N}/epsilon^2).

Keywords:Game theory, Large-scale systems, Optimization algorithms Abstract: We consider the problem to control a large population of noncooperative heterogeneous agents, each with strongly convex quadratic cost function depending on the average population state, and all sharing a convex constraint, towards a competitive equilibrium. We assume a minimal information structure through which a central controller can broadcast incentive signals to control the decentralized optimal responses of the agents. We propose a model-free dynamic control law that, based on monotone operator theory arguments, ensures global convergence to an equilibrium independently on the parameters defining the quadratic cost functions, nor on the convex constraints.

Keywords:Game theory, Communication networks, Control applications Abstract: Game theory, as a powerful conceptual framework, has in the past decade or so been widely applied to wireless communications in a variety of contexts. One such context is power control, where a game-theoretic formulation is particularly well-motivated since the distributed power control paradigm makes it natural to treat each wireless link (consisting of a transmitter and a receiver) as a player equipped with its own incentives. However, much of the work on game-theoretic studies of power control has been focused on one-shot games, where the emphasis is placed on either characterizing the existence and/or uniqueness of a Nash equilibrium or dynamics for reaching that Nash equilibrium

In this paper, we consider a repeated game framework for power control in wireless communications that captures the salient features of the repeated interactions between different wireless links. We present a unified presentation of both finitely and infinitely repeated games and discuss the interesting information structure special to the power control setting. We then consider in depth two classes of solution concepts: Subgame Perfect Nash Equilibrium (SPNE) and no-regret strategy. For the former, we characterize the existence and uniqueness/multiplicity of SPNE; for the latter, we take an online convex optimization approach and design a power control scheme that is no regret for a link (irrespective of what the other links do), with an explicit finite time regret bound. These two solution concepts not only serve the normative role (from an economic-theoretical standpoint) of explaining how the wireless links transmit power in repeated interactions, but also induce distributed power control schemes that enjoy desirable properties from an engineering standpoint. Finally, we study a special case (one with ``good" channel conditions) where we give a different power control strategy that both enjoys a more refined regret bound and converges to the unique Nash equilibrium of the stage game.

Keywords:Game theory, Computational methods, Autonomous systems Abstract: This study reveals a parametric representation of the equilibrium assessment of the Bayesian game, and proposes a method for computing player's beliefs when a BEN is given or measured as a game outcome. To obtain the parameterization, we employ a deterministic transition model in the state-space representation, proposed in our previous work, that transfers from a pair value of the beliefs and the BNE to a different pair value. Here, the pair is called an equilibrium assessment and becomes a state variable. We then perform a steady-state analysis of the model. The main contribution of this study is the fractional form of the resulting parameterization. Moreover, the ratio is unchanged by transitions of the equilibrium assessment in the model. On account of the constant ratio we can apply the parameterization to belief computation based on the measured BNE. Finally, a numerical example confirms that the correctness of the parameterization and its utility in computing the player's beliefs from the measured BNE. This computation should realize significant and unique developments; for example, a control-theoretic framework for a mechanism design in which players need not report their types or valuations (private information) to a principal.

Keywords:Optimal control, Nonlinear output feedback, Delay systems Abstract: This paper studies optimal control processes governed by a specific family of systems described by functional differential equations (FDEs) involving the sup-operator. Systems evolving with the state suprema constitute a useful abstraction for various models of technological and biological processes. The specific theoretic framework incorporates state suprema in the right hand side of the initially given differential equation and finally leads to a FDE with the state-dependent delays. We study a class of nonlinear FDE-featured optimal control problems (OCPs) in the presence of some additional control constraints. Our aim is to develop implementable first-order optimality conditions for the retarded OCPs under consideration. We use the celebrated Lagrange approach and prove a variant of the Pontryagin-like Minimum Principle for the given OCPs. Moreover, we discuss a computational approach to the main dynamic optimization problems and also consider a possible application of the developed methodology to the Maximum Power Point Tracking (MPPT) control of solar energy plants.

Keywords:Optimal control, Optimization, LMIs Abstract: This paper is devoted to the problem of optimal selection of a subset of available actuators/sensors through a multi-channel H2 dynamic output feedback controller for continuous linear time invariant systems. Incorporating two extra terms for penalizing the number of actuators and sensors into the optimization objective function, we develop an iterative process to identify the favorable row/column-wise sparse DOF gains. Employing the identified structure, we solve the constructed row/column structured multi-channel H2 DOF problem in order to derive a gain that exploits optimum number of sensors/actuators by which the closed-loop stability is maintained and the performance degradation of the closed-loop system is restricted. Through an example we demonstrate the remarkable performance and broad applicability of the proposed approach.

Keywords:Optimal control, Optimization algorithms, Flight control Abstract: We study an aircraft abort landing problem modelled by a five dimensional state system with state constraints and a maximum running cost function as introduced by Bulirsch, Montrone and Pesch (J. Optim. Theory Appl., Vol. 70, No 1, pp 1--23, 1991). We propose a Hamilton-Jacobi-Bellman (HJB) approach in order to compute the value function associated to the problem, as well as trajectory reconstruction procedures based on the value function, or on a related exit time function. Some numerical illustrations are included to show the relevance of our approach.

Keywords:Optimal control, Optimization algorithms, Numerical algorithms Abstract: This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints are already convex or convexified, the proposed algorithm convexifies the nonlinear dynamics, via a linearization, in a successive manner. Thus at each succession, a convex optimal control subproblem is solved. Since the dynamics are linearized and other constraints are convex, after a discretization, the subproblem can be expressed as a finite dimensional convex programming subproblem. Since convex optimization problems can be solved very efficiently, especially with custom solvers, this subproblem can be solved in time-critical applications, such as real-time path planning for autonomous vehicles. Several safe-guarding techniques are incorporated into the algorithm, namely virtual control and trust regions, which add another layer of algorithmic robustness. A convergence analysis is presented in continuous-time setting. By doing so, our convergence results will be independent from any numerical schemes used for discretization. Numerical simulations are performed for an illustrative trajectory optimization example.

Keywords:Optimal control, Optimization algorithms, Robotics Abstract: Trajectory optimization algorithms are a core technology behind many modern nonlinear control applications. However, with increasing system complexity, the computation of dynamics derivatives during optimization creates a computational bottleneck, particularly in second-order methods. In this paper, we present a modification of the classical Differential Dynamic Programming (DDP) algorithm that eliminates the computation of dynamics derivatives while maintaining similar convergence properties. Rather than relying on naive finite difference calculations, we propose a deterministic sampling scheme inspired by the Unscented Kalman Filter that propagates a quadratic approximation of the cost-to-go function through the nonlinear dynamics at each time step. Our algorithm takes larger steps than Iterative LQR—a DDP variant that approximates the cost-to-go Hessian using only first derivatives—while maintaining the same computational cost. We present results demonstrating its numerical performance in simulated balancing and aerobatic flight experiments.

Keywords:Optimal control, Power systems, Control of networks Abstract: We postulate the problem of optimal load shedding over multiple rounds to prevent cascading failure in power networks as a dynamic programming problem over a state space consisting of discrete and continuous variables, corresponding to link active status and demand-supply at the nodes respectively. We propose a generic branch and bound algorithm for this problem, and present tools to reduce the associated computational complexity. In particular, we adapt results on rank one perturbations of pseudo-inverse of Laplacian matrices to compute flow redistribution under link failure, and introduce monotonicity properties under which the set of control policies requiring consideration reduces to a considerably small set. These tools are illustrated in the context of proportional load shedding control and simple network topologies. Simulation results to compare the residual load under an optimal control policy and under an optimal proportional control policy, on a benchmark IEEE network, are also included.

Keywords:Optimization algorithms, Predictive control for linear systems, Numerical algorithms Abstract: In multiparametric programming an optimization problem which is dependent on a parameter vector is solved parametrically. In control, multiparametric quadratic programming (mp-QP) problems have become increasingly important since the optimization problem arising in Model Predictive Control (MPC) can be cast as an mp-QP problem, which is referred to as explicit MPC. One of the main limitations with mp-QP and explicit MPC is the amount of memory required to store the parametric solution and the critical regions. In this paper, a method for exploiting low rank structure in the parametric solution of an mp-QP problem in order to reduce the required memory is introduced. The method is based on ideas similar to what is done to exploit low rank modifications in generic QP solvers, but is here applied to mp-QP problems to save memory. The proposed method has been evaluated experimentally, and for some examples of relevant problems the relative memory reduction is an order of magnitude compared to storing the full parametric solution and critical regions.

Keywords:Optimization algorithms, Predictive control for linear systems, Predictive control for nonlinear systems Abstract: The alternating direction method of multipliers (ADMM) is an iterative first order optimization algorithm for solving convex problems such as the ones arising in linear model predictive control (MPC). The ADMM convergence rate depends on a penalty (or step size) parameter that is often difficult to choose. In this paper we present an ADMM prescaling strategy for strongly convex quadratic problems with linear equality and box constraints. We apply this prescaling procedure to MPC-type problems with diagonal objective, which results in an elimination of the penalty parameter. Moreover, we illustrate our results in a numerical study that demonstrates the benefits of prescaling.

Keywords:Optimization algorithms, Robotics, Hybrid systems Abstract: Virtual constraints have been recognized as an essential bridging tool which has the potential to translate rich nonlinear bipedal control methodologies to the control of prostheses. In this paper, we propose a hybrid system model based two-step direct collocation approach to automatically generate three-dimensional (3D) human-like multi-contact prosthetic gaits (via virtual constraints) for an asymmetric amputee-prosthesis system model. Unimpaired human locomotion is studied first to provide a reference for this gait design method. Specific requirements—such as amputee comfortability, human-likeness, physical limitations for hardware implementation—are then discussed explicitly in order to quantify a well-designed prosthetic gait. A 29 degrees of freedom 3D unsymmetrical bipedal robotic model is considered to model the asymmetric amputee-prosthesis system. Imposing the prosthetic gait requirements as nonlinear constraints and utilizing the asymmetric 3D hybrid system model, a two-step direct collocation based optimization method is proposed to generate 3D prosthetic gaits automatically. The resulting prosthetic gait is analyzed in detail, showing the designed multi-contact gait is human-like, formally stable and optimal w.r.t the requirements.

Keywords:Optimization algorithms, Robust control, Uncertain systems Abstract: This paper considers the problem of solving Quadratic Programs (QPs) in the context of robust Model Predictive Control (MPC) based on scenario trees. A Newton strategy is used in conjunction with dual decomposition, yield- ing a parallelizable method with a fast practical convergence. In this context, it has been observed that the Hessian of the dual function has an intricate sparsity structure and can be rank deficient, hence requiring a computationally expensive linear algebra and a regularization strategy. In this paper, we show that it is possible to organize the robust MPC problem such that the dual Hessian has a block-tridiagonal structure, hence reducing dramatically the cost of its factorization. Moreover, a simple and inexpensive strategy of constraint elimination is pro- posed for ensuring the positive definiteness of the dual Hessian, making regularization superfluous. This strategy additionally allows for evening the computational burden of computing the robust MPC solution in its parallelization.

Keywords:Optimization algorithms, Simulation, Stochastic optimal control Abstract: We propose an improved Hessian estimation scheme for the second-order random directions stochastic approximation (2RDSA) algorithm [1]. The proposed scheme, inspired by [2], reduces the error in the Hessian estimate by (i) incorporating a zero-mean feedback term; and (ii) optimizing the step-sizes used in the Hessian recursion of 2RDSA. We prove that 2RDSA with our Hessian improvement scheme (2RDSA- IH) converges asymptotically to the true Hessian. The advantage with 2RDSA-IH is that it requires only 75% of the simulation cost per-iteration for 2SPSA with improved Hessian estimation (2SPSA-IH) [2]. Numerical experiments show that 2RDSA-IH outperforms both 2SPSA-IH and 2RDSA without the improved Hessian estimation scheme.

Keywords:Optimization algorithms Abstract: In this work, we study the problem of keeping the objective functions of individual agents varepsilon-differentially private in cloud-based distributed optimization, where individual agents are subject to global constraints and seek to minimize local objective functions. The communication architecture between agents is cloud-based -- instead of communicating directly with each other, they coordinate by sharing states via a cloud computer. In this problem, the difficulty is twofold: the objective functions are used repeatedly in every iteration; the influence of perturbing them extends to other agents and lasts over time. To solve the problem, we analyze the propagation of perturbation on object functions over time, and derive an upper bound. With the upper bound, we design a noise-adding mechanism that randomizes the cloud-based distributed optimization algorithm to keep the individual objective functions varepsilon-differentially private. In addition, we study the trade-off between the privacy of objective functions and the performance of the new cloud-based distributed optimization algorithm with noise. We present simulation results to numerically verify the theoretical results presented.

Keywords:Stochastic systems, Finance, Uncertain systems Abstract: Kelly betting is a prescription for optimal resource allocation among a set of gambles which are typically repeated in an independent and identically distributed manner. In this setting, there is a large body of literature which includes arguments that the theory often leads to bets which are “too aggressive” with respect to various risk metrics. To remedy this problem, many papers include prescriptions for scaling down the bet size. Such schemes are referred to as Fractional Kelly Betting. In this paper, we take the opposite tack. That is, we show that in many cases, the theoretical Kelly-based results may lead to bets which are “too conservative” rather than too aggressive. To make this argument, we consider with a random vector X with its assumed probability distribution and draw m samples to obtain an empirically-derived counterpart Y. Subsequently, we derive and compare the resulting Kelly bets for both X and Y with consideration of sample size m as part of the analysis. This leads to identification of many cases which have the following salient feature: The resulting bet size using the true theoretical distribution for X is much smaller than that for Y. For these cases, it is then argued that the bet associated with X is far too conservative from a common sense point of view. If instead the bet is based on empirical data, “golden” opportunities are identified which are essentially rejected when the purely theoretical model is used. To formalize these ideas, we provide a result which we call the Restricted Betting Theorem. An extreme case of the theorem is obtained when X has unbounded support. In this situation, using X, the Kelly theory can lead to no betting at all whereas use of the empirical data-based distribution can lead to a significantly large fraction of one’s assets being at risk. Finally, the paper also includes numerical examples to illustrate the results which are given.

Keywords:Stochastic systems, Hybrid systems, Markov processes Abstract: Stochastic Hybrid Systems (SHS) constitute an important class of mathematical models that integrate discrete stochastic events with continuous dynamics. The time evolution of statistical moments is generally not closed for SHS, in the sense that the time derivative of the lower-order moments depends on higher-order moments. Here, we identify an important class of SHS where moment dynamics is automatically closed, and hence moments can be computed exactly by solving a system of coupled differential equations. This class is referred to as linear time-triggered SHS (TTSHS), where the state evolves according to a linear dynamical system. Stochastic events occur at discrete times and the intervals between them are independent random variables that follow a general class of probability distributions. Moreover, whenever the event occurs, the state of the SHS changes randomly based on a probability distribution. Interestingly for this class of linear TTSHS, the first and second-order moments depend only on the mean time interval between events and are invariant of their higher-order statistics. Finally, we discuss applicability of our results to different application areas such as network control systems and systems biology.

Keywords:Stochastic systems, Linear systems, Control applications Abstract: The stability of linear continuous-time systems with stochastic delay is investigated in this paper. The delay is assumed to be a piece-wise constant function of time such that it switches between finitely many different values stochastically. The stability of the stochastic system is assessed in terms of the convergence of the second moment of the state. Using infinite-dimensional solution operators, a stochastic linear map is constructed, allowing us to derive necessary and sufficient conditions of second moment stability. The discretization of the solution operators can be used to draw stability charts. An illustrative example is discussed to shed some light on the effects of stochastic delays on stability.

Keywords:Stochastic systems, Lyapunov methods, Network analysis and control Abstract: In this paper, directed graphs where the network topology is governed by a stochastic process are addressed. A one-to-one correspondence between these graphs and stochastic discrete-time systems, with set-valued transition map, is stated. Hence, by taking advantage of this equivalence, mathematical tools available for these discrete-time systems are used to characterize connectivity properties of stochastic digraphs. Namely, we characterize reachability in finite steps, reachability in infinite steps and recurrence relatively to a given set for a stochastic digraph in terms of auxiliary functions.

Keywords:Stochastic systems, Lyapunov methods, Stability of hybrid systems Abstract: This paper is concerned with the asynchronous control problem for a class of discrete-time semi-Markov jump linear systems via the semi-Markov kernel approach, where “asynchronous control” refers to a mismatch of the modes between the system and the mode-dependent controller resulting from one-step time delay in the mode switching of the controller. By employing a Lyapunov function dependent on both sojourn time and system mode, sufficient conditions on the existence of the desired mode-dependent controller are developed such that the closed-loop semi-Markov jump linear system is σ-error mean square stable. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control strategy.

Keywords:Stability of nonlinear systems, Markov processes, Stochastic systems Abstract: In this paper, we address finite-time partial stability in probability for nonlinear stochastic dynamical systems. Specifically, we provide Lyapunov conditions involving a Lyapunov function that is positive definite and decrescent with respect to part of the system state, and satisfies a differential inequality involving fractional powers for guaranteeing finite-time partial stability in probability. In addition, we show that finite-time partial stability leads to uniqueness of solutions in forward time and we establish necessary and sufficient conditions for almost sure continuity of the settling-time operator of the nonlinear stochastic dynamical system.

Keywords:Estimation, Statistical learning, Filtering Abstract: Motivated by a need in online advertising, where control systems often involve estimators of very small event rates, we propose an adaptive algorithm that regulates the stiffness of an otherwise time-invariant Bayesian event rate estimator to maintain a desired relative steady-state standard deviation of the event rate estimate. The result is an estimator that is fast (agile) when permitted by the observed input data, and that is slow (stiff) only when necessary to maintain the desired relative steady-state standard deviation of the estimate.

Keywords:Estimation, Stochastic systems, Kalman filtering Abstract: Several approaches have been developed to estimate probability density functions (pdfs). The pdf has two important properties: the integration of pdf over whole sampling space is equal to 1 and the value of pdf in the sampling space is greater than or equal to zero. The first constraint can be easily achieved by the normalisation. On the other hand, it is hard to impose the non-negativeness in the sampling space. In a pdf estimation, some areas in the sampling space might have negative pdf values. It produces unreasonable moment values such as negative probability or variance. A transformation to guarantee the negative-free pdf over a chosen sampling space is presented and it is applied to the nonlinear projection filter. The filter approximates the pdf to solve nonlinear estimation problems. For simplicity, one-dimensional nonlinear system is used as an example to show the derivations and it can be readily generalised for higher dimensional systems. The efficiency of the proposed method is demonstrated by numerical simulations. The simulations also show that, for the same level of approximation error in the filter, the required number of basis functions with the transformation is a lot smaller than the ones without transformation. This would largely benefit the computational cost reduction.

Keywords:Estimation, Switched systems, Time-varying systems Abstract: Many real world problems can be modeled by a linear Gaussian model with a slowly time-varying and abruptly changing regression coefficient (called the state). However, some practical applications don't allow us to get complete knowledge of state dynamics parameters a priori. We address state estimation of the linear Gaussian model whose state dynamics is represented by a special case of switched linear systems. We also present a new multiple model method with an online adaptive model set (called the bank) for estimating the state without knowing the parameters a priori. The method is based on recursive least squares (RLS) algorithms and switching detection. The bank consists of RLS algorithm modulated estimators. Each estimator adapts to each elemental linear system. A new estimator is generated and added to the bank every time a switching among the linear systems is detected. The state is estimated as a mixture of bank element estimations weighted by a posterior distribution of the elements. In terms of computational efficiency, the new estimator is generated in closed form and the posterior distribution, that is a non-convex function, is approximated as a discrete distribution with a small number of bins. Computer simulations show that our online bank adaptation method improves state estimation accuracy of a baseline method that don't employ online bank adaptation, and our multiple model method requires less computational resources to achieve a practicable state estimation than conventional multiple model methods that employ online Kalman Filter bank adaptation.

Keywords:Estimation, Uncertain systems, Nonlinear output feedback Abstract: This work presents the design and the corresponding stability analysis of a model free velocity observer formulation for nonlinear systems modeled by Euler-Lagrange formulation. The observation gains of the proposed formulation are tuned online according to an update algorithm removing the burden of observation gain tuning. Lyapunov based arguments are applied to prove the overall system stability. Performance of the observer proposed is illustrated via extensive simulation studies. Experimental studies are also utilized to demonstrate the viability of the proposed formulation.

Keywords:Estimation, Uncertain systems, Randomized algorithms Abstract: When the model of the system under observation is not precisely known, state estimation and the subsequent prediction of system trajectories from this state estimate is subject to uncertainty. A useful method state estimation and prediction is to provide bounds within which the estimates are guaranteed to lie. When a model set is available, predictions can be made for every element of this set, with bounds derived from these predictions. The goal of this work is to reduce the computational complexity of a robust moving horizon estimation (MHE) method of this from. The main element of this method is the computation and use of a so called approximate convex hull that provides an approximate cover of the model set. Estimates and predictions need only be made for the models at the vertices of the approximate convex hull. An output bound is given that reflects the effect of the approximation error. Therefore, the method guarantees that the actual output is in the bound estimated by the robust MHE.

Keywords:Estimation Abstract: The problem of estimating the n unknown amplitudes, frequencies and phases of the components of a multi-sinusoidal signal is addressed in this paper. The proposed methodology theoretically allows the exact identification of the above unknown parameters within an arbitrarily small finite time in the noise-free scenario. The measured signal is processed by a bank of Volterra integral operators with a suitably designed kernel, that yields a set of auxiliary signals which are computable on-line by causal linear filters. These auxiliary signals are in turn used to estimate the frequencies in an adaptive fashion, while the amplitudes and the phases estimates can be calculated by means of algebraic formulas. The effectiveness of the estimation technique is evaluated and compared with other existing finite-time estimators via numerical simulations.

Keywords:Identification, Time-varying systems Abstract: The on-line recursive estimation of linear time-varying systems usually involves discrete-time models. In the case of continuous-time models, recursive off-line estimation has been considered in some detail but on-line approaches based on continuous-time models have received less attention, partly due to the increased complexity associated with the need to handle the time-derivatives of the input and output variables. In this study, we present a real-time instrumental variable technique where linear filters are used to handle the time derivatives and the parameter variations are represented by a stochastic model.

Keywords:Identification, Time-varying systems Abstract: We extend the recently introduced regularization/Bayesian System Identification procedures to the estimation of time-varying systems. Specifically, we consider an online setting, in which new data become available at given time steps. The real-time estimation requirements imposed by this setting are met by estimating the hyper-parameters through just one gradient step in the marginal likelihood maximization and by exploiting the closed-form availability of the impulse response estimate (when Gaussian prior and Gaussian measurement noise are postulated). By relying on the use of a forgetting factor, we propose two methods to tackle the tracking of time-varying systems. In one of them, the forgetting factor is estimated by treating it as a hyper-parameter of the Bayesian inference procedure.

Keywords:Linear parameter-varying systems, Uncertain systems, Identification Abstract: In this paper, we introduce and study important properties of the transformation of Affine Linear Parameter-Varying (ALPV) state-space representations into Linear Fractional Representations (LFR). More precisely, we show that (i) state minimal ALPV representations yield minimal LFRs, and vice versa, (ii) the input-output behavior of the ALPV representation determines uniquely the input-output behavior of the resulting LFR, (iii) structurally identifiable ALPV models yield structurally identifiable LFRs, and vice versa. We then characterize LFRs which correspond to equivalent ALPV models based on their input-output maps. As illustrated all along the paper, these results have important consequences for identification and control of systems described by LFRs.

Keywords:Identification Abstract: This paper investigates the identification of Continuous-Time models based on binary observations. Currently, no identification algorithm has been proposed in this field. The reason is twofold: first the time-domain differentiation operator of a such model structure prevents the use of existing identification methods based on binary observations, second the simple knowledge of binary observations on the output prevents the use of existing Continuous-Time identification methods. In this paper a two steps identification algorithm is derived. It is based on the combined use of a specific input signal and Support Vector Machines for the reconstruction of a high resolution output signal. This high resolution output signal is then used for the estimation of a Continuous-Time model. An extension for the identification of a MISO system is also proposed. Some simulation results are given in order to illustrate the validity of the proposed method.

Keywords:Identification Abstract: In this paper we consider the problem of set-membership identification of nonlinear polynomial output error models, where output measurements are affected by bounded additive noise known to enjoy certain peculiar properties like whiteness and uncorrelation with the noiseless output sequence. More precisely, we propose an original approach to compute the so-called parameter uncertainty intervals by properly taking into account all the available a-priori information about the model structure and the properties of the noise. Parameters bounds are obtained by computing the solution to a set of polynomial optimization problems, where the decision variable are suitably selected and constrained in order to enforce the available a-priori information on the noise properties. Convex relaxation techniques are exploited to solve the formulated optimization problem. A simulation example is reported in order to show the effectiveness of the proposed approach.

Keywords:Identification Abstract: In this paper we propose a single-stage procedure for set-membership identification of nonlinear systems in Lur'e form, where the nonlinear block can be modeled by a polynomial with finite and known order. First the problem of computing parameter bounds is formulated in terms of polynomial optimization. Then, by suitably exploiting the peculiar sparsity structure of the problem, a computational efficient convex relaxation approach is proposed for approximating the global optimal solution of the formulated nonconvex optimization problem. The effectiveness of the presented algorithm is shown by means of a simulation example.

Keywords:Direct adaptive control, Adaptive control, Adaptive systems Abstract: We recently proposed a linear matrix inequalities-based hedging approach to compute stability limits of adaptive controllers in the presence of first-order actuator dynamics. Specifically, our approach modifies the ideal reference model dynamics using the hedging method to allow correct adaptation, which is not affected by the presence of actuator dynamics, and then analyzes the stability of this modified reference model coupled with the first-order actuator dynamics using linear matrix inequalities -- for computing the fundamental stability interplay between the bandwidth of actuator dynamics and the allowable system uncertainties. This paper generalizes this framework to high-order (linear time-invariant) actuator dynamics and discuss the distance between the uncertain dynamical system and the ideal (i.e., unmodified) reference model dynamics. An illustrative numerical example is provided to demonstrate the efficacy of the proposed approach in computing stability limits of adaptive controllers.

Keywords:Robust adaptive control, Adaptive control, Robust control Abstract: Here we consider the problem of providing near optimal LQR performance for a large set of admissible models. We consider the single-input single-output (SISO) setting, and prove that given a compact set of controllable and observable plant models of a fixed order, we can construct a single nonlinear periodic controller of low complexity which provides near optimal LQR performance for every admissible plant model. This controller is proven to provide strong linear-like bounds on the state behaviour.

Keywords:Robust adaptive control, Cooperative control, Output regulation Abstract: The global robust output regulation problem for nonlinear multi-agent systems in the output feedback form with uncertainty of a known bound has been studied in one of our previous papers by distributed output feedback control law i.e., a control law that features the nearest neighbor principle. This paper further studies the global robust output regulation problem for the same class of systems with arbitrarily large uncertainty by a combined robust and adaptive high gain technique. A recursive procedure is developed for constructing a decentralized output feedback control law. For systems with the relative degree smaller than 3, the decentralized output feedback control reduces to a distributed output feedback control law. The effectiveness of our approach is illustrated by a family of hyper-chaotic Lorenz systems.

Keywords:Adaptive control, Robotics, Robust control Abstract: In a recent SIAM Journal on Control and Optimization article, our team analyzed the robustness of a class of adaptive three-dimensional curve tracking controls for free moving particles, using penalty functions and robustly forwardly invariant sets with maximum allowable perturbation bounds. This allowed us to identify unknown control gains and provide predictable tolerance and safety bounds, under input delays. In this work, we provide a variant of our SIAM article. We provide a new method to maintain robust forward invariance of fixed compact regions in the state space, under arbitrarily large perturbation bounds. Our new technique entails scaling certain control components. It provides a substantially different algorithm from our SIAM article and is suitable for real time applications.

Keywords:Model Validation, Robust adaptive control Abstract: In most direct adaptive control techniques the dynamic order of systems are assumed to be known. However, this assumption in most real-world problems is not met. Fostered by addressing this problem, this paper presents a methodology to design an operational controller for a specific class of deterministic input-affine systems. Meaning, in the first phase the dynamic order of the unknown system is determined contingent upon a correlation-based heuristic criterion through exciting the system and gathering input-output data samples. Without any a priori knowledge about the system except the fact that its maximum order is less than a known number, with an intelligent search among all possible models, the suggested algorithm precisely identifies the dynamic order of the system. In the second phase, needless to estimate parameters of the system, a robust adaptive technique is designed to update parameters of the controller in order to track a bounded differentiable reference signal without chattering. The robustness and maximum error of the suggested control strategy for input-affine systems whose parameters are varying limitedly is also investigated. Effectiveness and pros-and-cons of the proposed approach are comprehensively discussed and shown through variety of simulations.

Keywords:Stability of nonlinear systems, Robust adaptive control, Uncertain systems Abstract: While non-smooth approaches (including sliding mode control) provide explicit feedback laws that ensure finitetime stabilization but in terminal time that depends on the initial condition, fixed-time optimal control with a terminal constraint ensures regulation in prescribed time but lacks the explicit character in the presence of nonlinearities and uncertainties. In this paper we present an alternative to these approaches, which, while lacking optimality, provides explicit time-varying feedback laws that achieve regulation in prescribed finite time, even in the presence of non-vanishing (though matched) uncertain nonlinearities. Our approach employs a scaling of the state by a function of time that grows unbounded towards the terminal time and is followed by a design of a controller that stabilizes the system in the scaled state representation, yielding regulation in prescribed finite time for the original state.

Keywords:Algebraic/geometric methods, Adaptive systems, Nonlinear systems identification Abstract: The persistence of excitation condition for signals generated by discrete-time, time-invariant, autonomous linear and nonlinear systems is studied. A rank condition is shown to be equivalent to persistence of excitation of signals generated by the class of systems considered, consistently with the results established by the authors for the continuous-time case. The condition is geometric in nature and can be checked a priori. The condition is geometric in nature and can be checked a priori for a Poisson stable system, that is, without knowing explicitly the state trajectories of the system. The significance of the ideas and tools presented is illustrated by means of simple examples.

Keywords:Algebraic/geometric methods, Autonomous robots, Nonholonomic systems Abstract: In this paper we investigate a model of two agents (self-steering particles) engaged in a dyadic interaction, with one pursuing the other using a constant bearing strategy. The pursued agent is controlled independently. Analysis of this interaction shows that the dynamics on the joint state space of the two agents restricts to an invariant manifold in shape space, and shares certain features in common with the Kepler problem. This model is applied to the task of tracking a stationary beacon with the practical constraint of using a sensor with a limited field of view (FOV). An effective solution to this problem is derived using the preceding analysis, and demonstrated in a laboratory implementation on a robot equipped with a Kinect vision sensor. Essential to this solution is the augmentation of the pursuit strategy (and associated feedback law) by an odometry-driven estimator when the beacon falls outside of the FOV.

Keywords:Algebraic/geometric methods, Biomedical, Pattern recognition and classification Abstract: Diffusion Tensor Imaging (DTI) generates a 3-dimensional 2-tensor field that encapsulates properties of diffusing water molecules. We present two complementing ideas that may be used to enhance and highlight geometric features that are present.The first is based on Ricci flow and can be understood as a nonlinear bandpass filtering technique that takes into account directionality of the spectral content. More specifically, we view the data as a Riemannian metric and, in manner reminiscent to reversing the heat equation, we regularize the Ricci flow so as to taper off the growth of the higher-frequency speckle-type of irregularities. The second approach, in which we again view data as defining a Riemannian structure, relies on averaging nearby values of the tensor field by weighing the summands in a manner which is inversely proportional to their corresponding distances of the tensors. The effect of this particular averaging is to enhance consensus among neighboring cells, regarding the principle directions and the values of the corresponding eigenvalues of the tensor field. This consensus is amplified along directions where distances in the Riemannian metric are short.

Keywords:Algebraic/geometric methods, Feedback linearization Abstract: We study flatness of two-input control-affine systems, defined on an n-dimensional state-space. We give a geometric characterization of systems that become static feedback linearizable after a two-fold prolongation of a suitably chosen control. They form a particular class of flat systems: they are of differential weight n + 4.

Keywords:Algebraic/geometric methods, Linear systems, Stability of linear systems Abstract: In this paper we show that the outer invariance entropy for admissible pairs of an affine system on a Lie group is given by the sum of the positive real parts of the eigenvalues of a derivation D* associated to the drift of the system.

Keywords:Algebraic/geometric methods, Lyapunov methods, Stability of nonlinear systems Abstract: Recently, a Finsler-Lyapunov function is provided for incremental stability analysis in the contraction framework. In this paper, by using this Finsler-Lyapunov function, we study differential input-to-state stability (ISS). Especially, we give sufficient conditions for differential ISS and differential integral ISS. An example demonstrates that a differential ISS condition can be used for synchronization analysis of a coupled oscillator.

Keywords:Nonlinear output feedback, Lyapunov methods, LMIs Abstract: Recently, a new strategy for local analysis of passivity indices and its application for output feedback asymptotic stabilization of nonlinear systems was proposed [2]. Polynomial input-affine systems were considered and sum of squares (SOS) techniques were employed for estimating a domain in which the passivity indices are valid and stability is guaranteed. Though simple and useful, the method still demands improvements, as the estimates obtained can be quite conservative. In this context, this work applies the Finsler's Lemma and the notion of linear annihilators for enlarging the estimates of the aforementioned regions of attraction by reformulating the estimation problem as a polytopic LMI condition. In addition, we extended the results of [2] for the class of the rational nonlinear systems with possibly rational Lyapunov functions. Numerical examples are also provided in order to demonstrate the applicability of the method.

Keywords:Nonlinear output feedback, Observers for nonlinear systems, Output regulation Abstract: A solution to the problem of global fixed-time output stabilization of a chain of integrators is proposed. A nonlinear state feedback and a dynamic observer are designed guaranteeing the fixed-time state control and estimation, respectively. Robustness with respect to exogenous disturbances and measurement noises is established. The performance of the obtained control and estimation algorithms are illustrated by numeric examples.

Keywords:Nonlinear output feedback, Output regulation, Optimization algorithms Abstract: This work proposes an iterative procedure for static output feedback of polynomial systems based on Sum-of- Squares optimization. Necessary and sufficient conditions for static output feedback stabilization of polynomial systems are formulated, both for the global and for the local stabilization case. Since the proposed conditions are bilinear with respect to the decision variables, an iterative procedure is proposed for the solution of the stabilization problem. Every iteration is shown to improve the performance with respect to the previous one, even if convergence to a local minimum might occur. Since polynomial Lyapunov functions and control laws are considered, a Sum-of-Squares optimization approach is adopted. A numerical example illustrates the results.

Keywords:Nonlinear systems identification, Identification Abstract: This paper discusses the problem of kernel selection in Reproducing Kernel Hilbert Spaces (RKHS) for nonlinear system identification and the use of a derivative norm regularization, in place of the traditional functional norm regularization.

However in the proposed formulation, an optimal representer for the estimated function cannot be defined. Here, this problem is investigated and a representer for the derivative regularization approach is proposed.

Additionally, we show how this permits a fully a priori choice of kernel function, determined completely independently of the data distribution and noise level.

The advantage of the proposed method is illustrated using two simulation examples, each presenting a scenario where the kernel selection is otherwise highly problematic: non-uniformly distributed data and functions of varying smoothness over the input space.

Keywords:Nonlinear systems identification, Switched systems, Identification Abstract: This paper considers the problem of switched Wiener system identification from a Kernel based manifold embedding perspective. Our goal is to identify both the Kernel mapping and the dynamics governing the evolution of the data on the manifold from noisy output measurements and with minimal assumptions about the nonlinearity and the affine portion of the systems. While in principle this is a very challenging problem, the main result of the paper shows that a computationally efficient solution can be obtained using a polynomial optimization approach that allows for exploiting the underlying sparse structure of the problem and provides optimality certificates. As an alternative, we provide a low complexity algorithm for the case where the affine part of the system switches only between 2 sub models.

Keywords:Differential-algebraic systems, Algebraic/geometric methods, Observers for nonlinear systems Abstract: This paper investigates observer design problem for a large class of nonlinear singular systems with multi outputs. We firstly regularize the singular system by injecting the derivative of outputs into the system. Then differential geometric method is applied to transform the regularized system into a simple normal form, for which a Luenberger-like observer is proposed.

Keywords:Discrete event systems, Supervisory control, Decentralized control Abstract: In decentralized discrete-event system (DES) architectures, agents fuse their local decisions to arrive at the global decision. The contribution of each agent to the final decision is never assessed; however, it may be the case that only a subset of agents, i.e., a (static) coalition, perpetually contribute towards the correct final decisions. In casting the decentralized DES control (with and without communication) problem as a cooperative game, it is possible to quantify the average contribution that each agent makes towards synthesizing the overall correct control strategy. Specifically, we explore allocations that assess contributions of non-communicating and communicating controllers for this class of problems. This allows a quantification of the contribution that each agent makes to the coalition with respect to decisions made solely based on its partial observations and decisions made based on messages sent to another agent(s) to facilitate a correct control decision.

Keywords:Discrete event systems, Supervisory control, Automata Abstract: We investigate the supervisor synthesis problem for centralized partially-observed discrete event systems subject to safety specifications. It is well known that this problem does not have a unique supremal solution in general. Instead, there may be several incomparable locally maximal solutions. One then needs a mechanism to select one locally maximal solution. Our approach in this paper is to consider a lower bound specification on the controlled behavior, in addition to the upper bound for the safety specification. This leads to a generalized supervisory control problem called the range control problem. While the upper bound captures the (prefix-closed) legal behavior, the lower bound captures the (prefix-closed) minimum required behavior. We provide a synthesis algorithm that solves this problem by effectively constructing a maximally-permissive safe supervisor that contains the required lower bound behavior. This is the first algorithm with such properties, as previous works solve either the maximally-permissive safety problem (with no lower bound), or the lower bound containment problem (without maximal permissiveness).

Keywords:Discrete event systems, Process Control, Computational methods Abstract: This paper demonstrates how the property of deadbeat controllers that drives discrete-time systems to their equilibria in a finite number of steps can be effectively used to develop systematic approximations of a certain class of heap systems, modeled here as input-quantized systems defined over the max-plus algebra. These systems are used to describe a class of flexible batch manufacturing processes that are important in applications such as chemical processing. The result here introduces a new, asymmetric approximation in the context of previous work where a symmetric approximation was developed and analyzed.

Keywords:Discrete event systems, Petri nets Abstract: Deterministically Synchronized Sequential Process (DSSP) are modular Petri Net (PN) systems composed by a set of state machines PNs (called also agents) cooperating through asynchronous message passing. The modular structure of DSSP allows strong analytical results, (for example, the rank theorem provides necessary and sufficient condition for structural liveness). This paper considers a synthesis problem of liveness enforcing. For some particular structures of DSSP in which the rank theorem does not hold we provide a technique based on the pre-assignment of the buffers in order to ensure that the model becomes live.

Keywords:Discrete event systems, Petri nets, Optimization Abstract: Timed Petri nets are commonly used for modelling and analysis of automated manufacturing systems, including batch or high throughput systems. This paper consider the cycle optimization problem for a deterministic timed weighted marked graphs under infinite server semantics. The problem aims to find an initial marking to minimize the cycle time while the weighted sum of tokens in places is less than or equal to a desired value. We transform a timed weighted marked graph into several equivalent timed marked graphs and present a mixed integer linear programming method which can provide an optimal solution. Meanwhile, two suboptimal methods are proposed to reduce the computational cost.

Keywords:Petri nets, Automata, Discrete event systems Abstract: In this paper we propose a novel approach to perform codiagnosability analysis of bounded Petri nets with arbitrary labeling functions. In more detail, a set of sites observe the system evolution, each one with its own observation mask. Sites do not exchange information with each other but communicate with a coordinator. The coordinator is able to detect a fault if and only if at least one site is able to do that. The proposed approach is based on a necessary and sufficient condition for codiagnosability, namely the absence of sequences that are ``ambiguous'' with respect to all sites and whose length may grow indefinitely after the occurrence of some fault (i.e., sequences of infinite length that could be observed either in the presence of a fault and with no fault). The novelties of the approach consist in using the notion of basis markings to avoid exhaustive enumeration of the set of reachable markings, and in the construction of an automaton, called Verifier, that enables to detect the presence of ambiguous sequences.

Keywords:Distributed parameter systems, Estimation Abstract: In many situations, a mobile sensor must traverse in hazardous environments to collect information about spatially distributed processes. Without any constraints, the sensor will be guided in spatial locations that tend to improve the performance of the state estimator. This translates to larger values of the state estimation error. Such a guidance is information-sensitive as the sensor seeks ``more'' useful information within the spatial region. However, when exposure to hazardous environments affect the reliability and life-expectancy of the sensor, then a modification to the guidance must be considered in order to increase the life-expectancy of the sensor. Assuming that the cumulative exposure to the spatial field has a limit, beyond of which the sensor is rendered inoperable, then a modification to the information-sensitive guidance is warranted in order to prolong the life of the sensor. This of course compromises the value of information as an information-averse guidance will certainly prolong the life of a sensor, but the sensor will provide measurements with reduced value for the estimator. These concerns are considered here and a sensor guidance scheme is proposed that provides information- sensitive guidance when the accumulated exposure is below a user-defined limit and then switches to an information- averse guidance in order to prolong the life-expectancy of the sensor. Numerical studies for a diffusion partial differential equation with a single mobile sensor are provided to provide some insights on the modified sensor guidance policy and its increased life expectancy.

Keywords:Distributed parameter systems, Cooperative control, Lyapunov methods Abstract: We consider mean-field equations, that are transport partial differential equations describing the evolution of the density of a crowd of interacting agents when their number grows to infinity.

We generalize the Jurdjevic-Quinn control strategy to such mean-field equations to achieve stability in a suitable sense. For instance, in the context of crowds, consensus or alignment of agents are among the most relevant goals and they correspond to stability to a suitable manifold.

Our main result is the definition of a Jurdjevic-Quinn strategy that is sparse, i.e. that acts on a small set of the configuration space at each time.

We show that such a stabilization strategy is adapted to achieve alignment of the kinetic Cucker-Smale model with a sparse control only.

Keywords:Neural networks, Distributed parameter systems, Optimal control Abstract: The computational issues involved in the solution of optimal control problems of propagating fronts described by level sets motivate the search for effective optimization algorithms. In this paper, we attack the problem of optimal control of moving fronts by searching for an approximate solution method that is computationally feasible and robust to local minima trapping. The presence of many local minima is a crucial difficulty one encounters in dealing with such a problem. Following previous results, we use the extended Ritz method to find approximate solutions. This approach consists in adopting a control law with fixed structure that depends nonlinearly on a number of parameters to be suitably chosen. To overcome the local minima issue, we propose to optimize the weights for the level set optimal control by a recursive minimization based on the extended Kalman filter (EKF). As compared with techniques based on gradient-descent methods, the EKF optimization turns out to be successful to reduce computational burden and increase robustness with respect to local minima trapping, as shown by simulation results in a test case involving a change of topology.

Keywords:Estimation, Modeling, Simulation Abstract: Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamard’s stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.

Keywords:Traffic control, Estimation, Nonlinear systems identification Abstract: Traffic State Estimation (TSE) refers to the estimation of a state, i.e., density, speed, or other state parameters, for vehicular traffic on roads based on partial observation data (e.g., road-side detectors and on-vehicle GPS devices). It can be used as a component in applications such as traffic control systems as a means to identify and alleviate congestion. In existing studies, the Kalman Filter and its extensions, notably the Ensemble Kalman Filter (EnKF), are commonly employed for TSE. Recently, the minimax filter has been newly adapted to this domain as a filtering algorithm for TSE as well. In this article, we compare the performance of EnKF and the minimax filter on discretized PDEs modeling traffic. Specifically, for the EnKF study, the estimation is performed using stationary and mobile sensor information based on actual traffic data, by employing EnKF in conjunction with a Godunov discretization of the Lighthill--Whitham--Richards (LWR) model. For the minimax study, the discontinuous Galerkin formulation of the LWR model is used in conjunction with the implicitly-linearized minimax filter to obtain state estimates using the same data. The advantages and disadvantages of each of the filters are empirically quantified. Insights for practical application and future research directions are presented.

Keywords:Sensor networks, Distributed parameter systems, Estimation Abstract: The aim if this paper is to develop a method for optimal node activation in large-scale sensor networks whose measurements are supposed to be used to estimate unknown parameters of the underlying distributed parameter system. Given a partition of the observation horizon into a finite number of consecutive intervals, the problem consists in selecting gaged sites on each interval so that the determinant of the Fisher information matrix associated with the estimated parameters be maximal. A major novelty here is that the numbers of active sensors may differ from interval to interval in accordance with the amount of information about the parameters expected in these intervals. An additional requirement is that, given a spatially-varying cost of taking measurements, the resulting total cost of the experiment must not exceed a fixed budget. The combinatorial nature of the sensor selection problem is circumvented by operating on the spatial density of sensors, rather than on the sensor locations. The original problem then reduces to maximizing the determinant of the sum of finite convex combinations of some nonnegative definite matrices subject to a linear inequality constraint reflecting the limited experimental budget and additional box constraints on the weights of this combination. Some separability characterizations of optimal solutions are indicated and then simplicial decomposition is applied to obtain numerical solutions. As a result, a simple computational scheme is obtained which can be implemented without resorting to sophisticated numerical software.

Keywords:Sampled-data control, Computational methods, Stability of hybrid systems Abstract: The paper provides computation-oriented necessary and sufficient conditions for the global exponential stability of linear systems with asynchronous sensors and actuators. Precisely, we focus on continuous-time linear systems whose state undergoes finite jumps referred to as impulsions. The impulsions are of two types: those related to input updates and those related to measurement updates. We assume that impulsions of each type occur periodically but the periods may be different and the clocks at the sensor and at the actuator are not synchronized. We first show that the analysis can be reduced to a finite time domain. Based on that, we provide necessary and sufficient conditions for the global exponential stability of systems belonging to the class under study. An example illustrates numerically the proposed results.

Keywords:Sampled-data control, Linear systems, Observers for Linear systems Abstract: We present a general sampled observability result for linear systems under not necessarily periodic sampling and furthermore illustrate its applicability in a number of problems which are of interest in their own right. We consider, with the general sampled observability result at hand, the problem of non-pathological sampling in multitarget tracking and the problem of non-pathological sampling of a class of switched linear systems. It is shown that for both problem types, the consideration of non-periodic sampling schemes is crucial, and that the general sampled observability result provides a particularly flexible and suitable tool to address these kinds of problems.

Keywords:Sampled-data control, Linear systems, Robust control Abstract: This paper studies the problem of tracking or disturbance rejection for sampled-data control systems, where the tracking signal can have frequency components higher than the Nyquist frequency. In view of the well-known sampling theorem, one recognizes that any high-frequency components may be detected only as an alias in the low base band, and hence impossible to recover or detect such frequency components.

This paper examines the basic underlying assumption, and show that it depends crucially on the underlying analog model. We show that it is indeed possible to recover such high-frequency signals, and also that, by introducing multirate signal processing techniques, it is possible to track or reject such frequency components. Detailed analysis of multirate closed-loop systems and zeros and poles are given. It is shown via examples that tracking of high-frequency signals beyond the Nyquist frequency can be achieved with satisfactory accuracy.

Keywords:Sampled-data control, Linear systems, Robust control Abstract: This paper is concerned with the Hankel operator and the Hankel norm of sampled-data systems. Even though these systems are intrinsically periodically time-varying, no studies have taken this important feature into account in the treatment of the Hankel operator,slash,norm. We characterize the Hankel operator,slash,norm of sampled-data systems adequately under the treatment with the L_2-type norm for the past input and the L_infty-type norm for the future output. Such treatment still captures the essential issue on the periodicity but contributes to neat arguments compared with the case when the L_2-type norm were also considered on the future output.

Keywords:Sampled-data control, Predictive control for linear systems, Mechatronics Abstract: A plant with unstable zeros is considered to be difficult to control because of initial undershoot of step response and unstable poles of its inversion system. A plant may have unstable zeros in discrete time domain because of following reasons: 1) non-collocation of actuators and sensors and 2) discretization by zero-order hold. We proposed a solution for these problems by using a multirate feedforward control with state trajectory generation based on time axis reversal. However, this method requires preactuation for negative infinite time. This paper proposes a state trajectory regeneration method via redundant order polynomial for the negative finite time. Although this method abandons perfect tracking during preactuation, it guarantees perfect tracking for a positive time domain. Moreover, the tracking error during finite time preactuation is reduced by the regenerated state trajectory obtained by the optimized redundant order polynomial. The validity of the proposed method is demonstrated through simulations.

Keywords:Sampled-data control, Time-varying systems, Linear systems Abstract: This paper provides a theoretical basis for discretization approaches to sampled-data systems in the L_infty/L_2 optimal controller synthesis problem. Such approaches have been developed through the lifting treatment for the corresponding analysis problem and allowed us to compute the induced norm in an asymptotically exact fashion as the parameter M tends to infty in the discretization processes of the generalized plant. This paper aims at establishing that these approaches are actually meaningful equally in the synthesis problem. To this end, we introduce important inequalities independent of the discrete-time controller, which are constructed through the fast-lifted representation of sampled-data systems; this representation employs the aforementioned parameter M, by which the sampling interval [0,h) is divided into M subintervals with an equal width without losing any information about the signals on the interval. Through these inequalities, we can verify that the discretization methods in our preceding study give a theoretical basis for tackling the optimal controller synthesis problem of minimizing the induced norm from L_2 to L_infty in SISO LTI sampled-data systems.

Keywords:Predictive control for nonlinear systems, Optimal control, Chemical process control Abstract: This paper proposes a method to surpass the computational hurdles associated with nonlinear model predictive control (NMPC) via a formulation of advanced-step bilinear Carleman approximation-based MPC (ACMPC). This formulation is a combination of bilinear Carleman approximation (also known as Carleman linearization) based MPC (BCMPC) and advanced-step nonlinear MPC (asNMPC). It takes action based on a prediction of the future initial state, reduces the amount of computation by analytically predicting future system behavior and providing the sensitivity of the cost function to the manipulated variables as the search gradient. Through a linear approximation, it updates the pre-calculated optimal control signals as soon as the real system states are obtained on-line. Thus, it significantly reduces the required time of computing the optimal control signals on-line before they are injected into the system. Regulating an open loop unstable CSTR under disturbance is illustrated as a case-study example.

Keywords:Predictive control for nonlinear systems, Stability of nonlinear systems, Lyapunov methods Abstract: A globally stabilizing nonlinear predictive control (NMPC) framework is developed by a simple design of the terminal cost used in relevant optimization setup.We first adapt the recent results on the finite horizon state-dependent Riccati equation (SDRE) based control for unconstrained nonlinear systems to prove that such a control can be globally stabilizing in case a sufficiently large optimization horizon is selected. Then, we use the resulting globally stabilizing Lyapunov function as a terminal cost within the optimization setup to get a novel NMPC. We also adapt the results on the stability of the NMPC, based on the control Lyapunov function approach to prove global stability of the proposed control framework. The results are validated through extensive simulation setups for some unconstrained nonlinear dynamical systems.

Keywords:Pulp and Paper Control, Predictive control for nonlinear systems, Process Control Abstract: We present a multiobjective economic model predictive control (m-econ MPC) strategy to mitigate high electrical energy demands of a two-stage mechanical pulping (MP) process. The nonlinear MP process considered in this paper consists of a primary and a secondary refiner. In the proposed m-econ MPC technique, economic performance is optimized during dynamic transitions while a stabilizing constraint is used to ensure convergence to steady-state operating points. Through simulations, we demonstrate that the m-econ MPC can reduce the energy consumed by mechanical pulping processes by up to 27%.

Keywords:Predictive control for nonlinear systems, Uncertain systems, Biological systems Abstract: This work deals with the problem of trajectory tracking for a nonlinear system with unknown but bounded model parameters uncertainties. First, this work focuses on the design of classical robust nonlinear model predictive control (RNMPC) law subject to model parameters uncertainties implying solving min-max optimization problem. Secondly, a new approach is proposed, consisting in approaching the basic min-max problem into a more tractable optimization problem based on the use of linearization techniques, to ensure a good trade-off between tracking accuracy and computation time. The robust stability of the closed-loop system is addressed. The developed strategy is applied to a simplified macroscopic continuous photobioreactor model, obtained from mass balance based modelling. Finally, the proposed control law is compared to the RNMPC controller. Its efficiency is illustrated through numerical results and robustness against parameter uncertainties is discussed for the worst case model mismatch.

Keywords:Predictive control for nonlinear systems, Hybrid systems, Identification for control Abstract: The safe and effective operation of Li-ion batteries requires Advanced Battery Management Systems (ABMSs), which can be designed by Model Predictive Control (MPC). The dynamics of Li-ion batteries are well described by a set of highly nonlinear and tightly coupled partial differential algebraic equations that arise from porous electrode theory, but the expressions are too complex to be included in the real-time optimization calculations carried out by MPC. For this reason, a linearized version of such models has been used in past studies. Such linear models do not describe all of the important dynamic nonlinearities of Li-ion battery operations, especially with regard to thermal management, and such plant-model mismatch can degrade performance and lead to violation of operational constraints. This paper proposes a Hybrid MPC (HMPC) algorithm that incorporates a PieceWise Affine AutoRegressive eXogenous (PWARX) battery model constructed using a tailored clustering and identification algorithm. Simulations show that this model better approximates the thermal behavior of the Li-ion cell, and obtains better closed-loop performance when compared to MPC based on an ARX model.

Keywords:Predictive control for nonlinear systems Abstract: We propose an approximate explicit model predictive control (MPC) scheme based on ideas in robust MPC. For every subset in a partial partition of the state space we solve a robust MPC problem offline, where the (only) uncertainty is the initial condition which may be any state in this particular subset. As a consequence, the control law defined by the solution of the MPC problem is valid for any state in the subset. The online computational effort reduces to a point location problem and application of the pre-computed MPC solution.

Keywords:Uncertain systems, Computational methods, Optimization Abstract: The efficient verification that the current state of an uncertain nonlinear system leads to a state in a target set at the next time instant is a practically important, yet theoretically challenging task. Fields of applications span from automatic driving in uncertain environments, human robot interaction with safety constraints, to event-triggered control. Based on newly developed relationships between an uncertain linear fractional transform and (skewed) structured singular values, we derive the maximum box of states in the admissible set and tests to check the robust admissibility. The results are illustrated by numerical examples, and are applied to event-triggered state feedback control.

Keywords:Uncertain systems, Computational methods, Stability of nonlinear systems Abstract: This paper presents a new numerical method to bound the location of the operating equilibrium of a nonlinear system subject to bounded parameter uncertainty and assure local stability. For this, sufficient conditions which guarantee the existence of an equilibrium within a bounded subset of state space for all parameter combinations and which prove that the location of this equilibrium is a continuous function of the parameters are derived. The conditions are verified numerically with reliable computing techniques that enable the numerical evaluation of functions and their derivatives on sets, yielding conservative results. A polytopic linear system that contains the linearized system dynamics at the operating equilibrium is obtained as part of the computation, and its stability is established with standard methods.

Keywords:Uncertain systems, Hybrid systems, Stability of hybrid systems Abstract: Global robust stabilization by sampled-data output feedback is investigated for a family of uncertain nonlinear systems. The nonlinear system under consideration has an internnect structure, consisting of a possibly unstable zero-dynamics with uncertainty and a driving system. Under a linear growth condition on the uncertain driven system and a Lipschitz condition on the driving system, we prove that there is a sampled-data, output feedback controller globally robustly stabilizing the uncertain nonminimum-phase system. The sampled-data output feedback compensator is designed by emulated versions of continuous-time observer and state feedback law, i.e., by holding the input/output signals constants over each sampling interval. The sampled-data controller consists of a discrete-time observer and controller whose construction relies only on the information of the nominal system of the controlled plant. Global robust stability of the hybrid closed-loop system with uncertainty is achieved by feedback domination, together with the robustness of the nominal closed-loop system.

Keywords:Uncertain systems, Linear systems, Robust control Abstract: We propose a novel method of jointly computing feedback controllers and associated robust invariant sets for discrete-time uncertain time-varying affine systems. The sets are parameterized as Minkowski sums of scaled and translated base sets and the control inputs as interpolations between control values at the vertices of the base sets. Robust invariance is enforced by a set of linear constraints. Various objectives can be approximated with the proposed method by specifying suitable convex cost functions, such as maximization and minimization of the resulting invariant sets, and optimization of the worst-case closed-loop performance.

Keywords:Uncertain systems, Observers for Linear systems, Electrical machine control Abstract: Interval observers are emerging methods for the state estimation of dynamical systems, especially if guaranteed error bounds are of interest as in the case of safety-critical systems. One class of systems that is of particular interest for real applications are LPV systems but so far, only a few approaches for interval observers for LPV systems have been proposed. In this paper, we extend the class of LPV systems for which interval observers can be designed under real operating conditions. We propose an interval observer that is based on a particular time-variant change of coordinates. The behavior of the presented interval approach is shown by numerical simulations of an induction machine.

Keywords:Uncertain systems, Optimization, Numerical algorithms Abstract: Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe interactions with the environment exactly; however, one must still guarantee that the model, despite uncertainty, behaves acceptably. This paper presents a convex optimization method to compute the set of configurations of a polynomial dynamical system that are able to safely reach a user defined target set despite parametric uncertainty. Since planning in the presence of uncertainty can lead to undesirable conservativeness, this paper computes those trajectories of the uncertain nonlinear systems that are alpha-probable of reaching the desired configuration. The presented approach uses the notion of occupation measures to describe the evolution of trajectories of a nonlinear system with parametric uncertainty as a linear equation over measures whose supports coincide with the trajectories under investigation. This linear equation is approximated with vanishing conservatism using a hierarchy of semidefinite programs each of which is proven to compute an approximation to the set of initial conditions that are alpha-probable of reaching the user defined target set safely despite uncertainty. The efficacy of this method is illustrated on three systems with parametric uncertainty.

Keywords:Power systems, Smart grid, LMIs Abstract: This paper presents an augmented optimal power flow (OPF) formulation that minimizes a power network's transient control costs using a linear quadratic regulator (LQR). The network is described by AC power flows with third-order generator dynamics modeling. Then, linearized dynamics around a known solution of the power flow equations are considered. Leveraging the equivalent linear matrix inequality formulation for the LQR, the augmented OPF (LQR-OPF) amounts to a semidefinite program, yielding optimal network steady state and an explicit feedback gain for minimum transient control cost. Numerical tests on a standard power network demonstrate the advantage of LQR-OPF in comparison to a scheme where OPF and transient control are solved separately.

Keywords:Power systems, Distributed control, Stability of nonlinear systems Abstract: This paper investigates the problem of optimal frequency regulation of multi-machine power networks where each synchronous machine is described by a sixth order model. By analyzing the physical energy stored in the network and the generators, a port-Hamiltonian representation of the multi-machine system is obtained. Moreover, it is shown that the open-loop system is passive with respect to its steady states which allows the construction of passive controllers to control the multi-machine network. As a special case, a distributed consensus based controller is designed that regulates the frequency and minimizes a global quadratic generation cost in the presence of a constant unknown demand. In addition, the proposed controller allows freedom in choosing any desired connected undirected weighted communication graph.

Keywords:Power systems, Electrical machine control Abstract: In this paper, we investigate the properties of an improved swing equation model for synchronous generators. This model is derived by omitting the main simplifying assumption of the conventional swing equation. We carry out a nonlinear analysis for the stability and frequency regulation and provide region of attraction estimates for two scenarios. First we study the case that a synchronous generator is connected to a constant load. Second, we inspect the case of the single machine connected to an infinite bus. Finally, the different behaviors of the conventional and improved swing equations are depicted by simulations.

Keywords:Power systems, Stability of linear systems, Optimization Abstract: Increased power transfers over a wide geographical area impact the small-signal stability of the power system, defined as the ability to damp oscillations between generators in different geographical areas. Wide-area control architectures have been proposed to control the generators in order to mitigate these oscillations. Ensuring that all unstable oscillating modes are removed depends on selecting a subset of generators to participate in wide-area control, which is inherently a discrete optimization problem that in the current literature does not have any solution algorithms with provable stability guarantees. In this paper, we present MinGen, a submodular optimization framework for generator selection for small-signal stability. We prove that small-signal stability is achieved when the unstable modes are controllable and observable from the set of selected generators, and map these properties to submodular constraints. We develop a computationally efficient and submodular MinGen algorithm with provable optimality bounds for generator selection, which can be generalized to enhance robustness to communication link failures. We evaluate our approach via a numerical study on the IEEE New England test case.

Keywords:Power systems, Stability of nonlinear systems Abstract: The problem of deriving verifiable conditions for stability of the equilibria of a realistic model of a synchronous generator with constant field current connected to an infinite bus is studied in the paper. Necessary and sufficient conditions for existence and uniqueness of equilibrium points are provided. Furthermore, sufficient conditions for almost global attractivity are given. To carry out this analysis a new Lyapunov-like function is proposed to establish convergence of bounded trajectories, while the latter is proven using the powerful theoretical framework of cell structures pioneered by Leonov and Noldus.

Keywords:Power systems, Stability of nonlinear systems Abstract: This paper analyzes the stability of a power system in which a synchronous generator and a photovoltaic (PV) generator supply the power to an infinite bus. The infinite bus corresponds to a large system to which the two generators are connected. The problem considered here is to investigate the existence of the equilibrium points of the system and their stability. For the problem, we derive a sufficient condition on the magnitude of the PV current for the existence of the equilibrium points. In addition, we analyze the stability of the equilibrium points, and show that the equilibrium points found under the derived condition are stable. These results clarify the impact of the penetration of the PV generator on the existence of the stable equilibrium points of the system.

Keywords:Aerospace Abstract: This paper investigates an augmented pure proportional navigation-based guidance strategy, which expands upon the need for precise control of the terminal approach and/or impact angle of an interceptor by also accounting for the maneuvering target’s ability to counter attack, e.g., in air-to-air combat. Specifically, an anticipatory modulation of the augmentation parameter is presented and analyzed, which addresses the objective of ensuring that the pursuer avoids any approaches that would place it within the evader’s own sights. Simulation results are developed and presented to support the theoretical findings.

Keywords:Aerospace Abstract: This paper presents a novel path following algorithm for unmanned aerial vehicles in the presence of external wind disturbances. The issue of input saturation due to turn radius constraints is addressed using the theory of nested saturation which is important for real-world systems. Furthermore, the proposed algorithm incorporates inertial speed that adds an adaptive capability to accommodate vehicle speed changes due to wind. The stability of the proposed algorithm is established through Lyapunov stability analysis. A comparative study is also performed to evaluate the performance of the proposed law with some existing algorithms.

Keywords:Aerospace, Observers for nonlinear systems, Hybrid systems Abstract: We present a uniformly globally exponentially stable hybrid angular velocity observer for rigid body systems designed directly on SO(3) x R^3. The global exponential stability result makes this observer a good candidate for a controller-observer combination with a guaranteed separation property. Simulation results are provided to demonstrate the effectiveness of the proposed hybrid observer as a part of an attitude stabilization scheme.

Keywords:Aerospace, Flight control, Stability of nonlinear systems Abstract: This paper proposes a guidance law that achieves the desired terminal impact time without violating a seeker's field-of-view (FOV) limits. In order to derive the guidance law, kinematic conditions for impact time control are defined, and the backstepping control technique is applied for the satisfaction of the conditions. As a virtual control input for the backstepping structure, the relative closing velocity is used and its magnitude is limited by a prescribed limit. Then, the seeker's look angle can also be confined within a specific range because the look angle is mainly determined by the difference between the line-of-sight (LOS) and the velocity vector. This capability to confine the seeker's look angle with achievement of the desired impact time is the main contribution of the paper. To evaluate the performance of the proposed law, numerical simulation is conducted. The result demonstrates that the proposed guidance law enables the missile to simultaneously achieve the zero miss distance and desired impact time without violating the prespecified FOV limits.

Keywords:Aerospace, Automotive control, Observers for nonlinear systems Abstract: This paper presents an acceleration control of a hexarotor unmanned aerial vehicle (UAV) in the earth-fixed frame with a disturbance observer (DOB). Unlike conventional cascade control structures where the outer-loop position controller generates the desired attitude command, the position controller in this paper generates the desired acceleration command in X, Y, Z axis of the earth-fixed frame. With acceleration control combined with DOB, the UAV could manage the lateral disturbance force that makes the trajectory tracking very challenging. This is a new concept compared with existing DOB-based UAV control approaches which aim to cancel the moment disturbance for precise attitude control. The small-gain theorem is used for stability analysis and Q-filter bandwidth design. Both simulation and actual experiment are shown to validate the performance of the proposed design.

Keywords:Aerospace, Robotics, Spacecraft control Abstract: We present a constrained trajectory generation approach for differentially flat systems that contain both time and frequency objectives. The algorithm extends an existing trajectory planning approach that combines nonlinear control theory, spline theory, and nonlinear programming. A space robotics example of constrained path planning is used to illustrate our method.

Keywords:Biological systems, Delay systems, Switched systems Abstract: In order to increase their robustness against environmental fluctuations, many biological populations have developed bet hedging mechanisms in which the population `bets' against the presence of prolonged favorable environmental conditions by having a few individual behaving as if they sensed a threatening or stressful environment. As a result, the population (as a whole) increases its chances of surviving environmental fluctuations in the long term, while sacrificing short-term performance. In this paper, we propose a theoretical framework, based on Markov jump linear systems, to model and evaluate the performance of bet-hedging strategies in the presence of stochastic fluctuations. We illustrate our results using numerical simulations.

Keywords:Biomolecular systems, Genetic regulatory systems Abstract: During mRNA translation, the ribosomal density profile along the coding region of the mRNA molecule affects various fundamental intracellular phenomena. Thus, steering this profile from a given to a desired density is an important biological problem. This paper studies this problem using a dynamical model for mRNA translation, called the ribosome flow model (RFM), in which one views the transition rates along the mRNA molecule as controls.

Keywords:Biological systems, Network analysis and control, Emerging control applications Abstract: The problem of emergent synchronization patterns in a complex network of coupled oscillators has caught scientists’ interest in a lot of different disciplines. In particular, from a biological point of view, considerable attention has been recently devoted to the study of the human brain as a network of different cortical regions that show coherent activity during resting-state. In literature, there can be found different large-scale models of resting-state dynamics in health and disease. In this context, the Kuramoto model, a classical model apt to describe oscillators’ dynamics, has been extended to capture the spatial displacement and the communication conditions in such brain network. Starting from a previous work in this field [1], we analyze this modified model and compare it with other existing large-scale models. In doing so, our aim is to promote a set of mathematical tools useful to better understand real experimental data in neuroscience and estimate brain dynamics.

Keywords:Biological systems, Optimal control, Modeling Abstract: This article presents a geometric and numerical approach to compute the optimal swimming strokes of a larval copepod. A simplified model of locomotion at low Reynolds number is analyzed in the framework of Sub-Riemannian geometry. Both normal and abnormal geodesics are considered along which the mechanical power dissipated by the swimmer is conserved. Numerical simulations show that, among various periodic strokes, a normal stroke consisting of a simple loop shape is maximizing the efficiency.

Keywords:Cellular dynamics, Pattern recognition and classification, Formal verification/synthesis Abstract: Embryonic stem cells (ESC) are generally regarded as the smallest functional units necessary to reproduce multicellular systems such as tissues and organs. Recent work showed that agent-based models of the stochastic dynamics of locally interacting stem cell agents accurately capture the time-dependent distributions of a variety of spatial patterns. Starting from a 3-dimensional, local interaction model of ESC proliferation and differentiation, in this paper, we developed a pattern classification and parameter optimization approach to maximize the occurrence of desired morphogenic patterns. Our approach uses Particle Swarm Optimization (PSO) and a pattern classification method that exploits a quantitative characterization of pattern formation. Since patterning likely imprints subsequent choices that stem cell aggregates make in lineage specification (e.g. precursors of neurons, lung cells, or muscle cells), our parameter optimization approach can be used to synthesize global differentiation patterns through local cues.

Keywords:Genetic regulatory systems, Biological systems, Stochastic optimal control Abstract: This paper is concerned with obtaining the infinite-horizon control policy for partially-observed Boolean dynamical systems (POBDS) when measurements take place in a finite observation space, with application to Boolean gene regulatory networks. The goal of control is to reduce the steady-state mass of undesirable states, which might be associated with disease. The idea behind the proposed method is to transfer the partially-observed Boolean states into a continuous observed state space known as belief space, and then employ the well-known value iteration method based on Point-Based Value Iteration (PBVI). The performance of the method is investigated using a Boolean network model constructed from melanoma gene expression data observed through Bernoulli noise.

Keywords:Energy systems, Distributed control, Decentralized control Abstract: In this paper, we propose a generation control strategy for islanded lossless microgrids with inverter-interfaced generators. In particular, we address the problem of obtaining a desired active power load sharing while regulating the frequency to some nominal value. The proposed control strategy is based on the slow readjustment of the active power reference of each inverter, i.e., each inverter aims to track a slowly-varying reference that is set sufficiently close to the actual active power injection, and, thus easy to track. The control enforces the trajectory to satisfy the so-called phase-cohesiveness property, i.e., the absolute value of the voltage phase angle difference across electrical lines is smaller than pi/2, which ensures the system remains stable at all times, while achieving the desired active power load sharing. We also propose a method to find the active power reference distributively which satisfies the phase-cohesiveness property for tree networks as well as for some cyclic networks.

Keywords:Energy systems, Power systems, Smart grid Abstract: We investigate the ability of a homogeneous collection of deferrable energy loads to behave as a battery; that is, to absorb and release energy in a controllable fashion up to fixed and predetermined limits on volume, charge rate and discharge rate. We derive bounds on the battery capacity that can be realized and show that there are fundamental trade-offs between battery parameters. By characterizing the state trajectories under scheduling policies that emulate two illustrative batteries, we show that the trade-offs occur because the states that allow the loads to absorb and release energy at high aggregate rates are conflicting.

Keywords:Energy systems, Control applications, Distributed control Abstract: This paper presents a study of cooperative power supply and storage for a network of Lithium-ion battery energy storage systems (LiBESSs). We propose to develop a distributed model predictive control (MPC) approach for two reasons. First, able to account for the practical constraints of a LiBESS, the MPC can enable a constraint-aware operation. Second, a distributed management can cope with a complex network that integrates a large number of LiBESSs over a complex communication topology. With this motivation, we then build a fully distributed MPC algorithm from an optimization perspective, which is based on an extension of the alternating direction method of multipliers (ADMM) method. A simulation example is provided to demonstrate the effectiveness of the proposed algorithm.

Keywords:Energy systems, Power systems, Optimization Abstract: Flexible loads can provide services such as load-shifting and regulation to power system operators through demand response. A system operator must know the aggregate capabilities of a load population to use it in scheduling and dispatch routines such as optimal power flow and unit commitment. It is not practical for a system operator to model every single load because it would compromise tractability and require potentially unavailable information. A key challenge for load aggregators is to develop low-order models of load aggregations that system operators can use in their operating routines.

In this paper, we develop a simple approximation for loads modeled by linear, second-order cone, and semidefinite constraints. It is an outer approximation of the Minkowski sum, the exact computation of which is intractable. We apply the outer approximation to loads with convex quadratic apparent power constraints and uncertainty modeled with second-order cone constraints.

Keywords:Energy systems, Stochastic optimal control, Predictive control for nonlinear systems Abstract: This paper presents a model predictive control (MPC)-based spatio-temporal optimization strategy that is applied to the problem of optimizing the altitude of an airborne wind energy (AWE) system. Altitude optimization for AWE systems represents a challenging problem under which the wind speed at the operating altitude dictates the net power produced by the system. The wind speed varies with both time and altitude and is typically only instantaneously observable at the operating altitude of the AWE system. The MPC strategy proposed in this work avoids the need for a computationally expensive Markov process model for characterizing the wind speed and is structured in a way that the need for instantaneous power maximization (termed exploitation) is balanced with the need to maintain an accurate map of wind speed vs. altitude (termed exploration). The MPC strategy is calibrated through data-driven statistical characterizations of the wind profile and is validated through real wind speed vs. altitude data.

Keywords:Energy systems, Stochastic optimal control, Smart grid Abstract: We study the optimal operation of energy storage operated by a consumer who owns intermittent renewable generation and faces (possibly random) electricity prices and different types of AC/DC load. We formulate the optimal storage operation problem as a finite-horizon dynamic program, with an objective of minimizing the expected energy cost. The incorporation of different types of AC/DC energy sources and appliances complicates the sequential decision making problem on storage operation. We provide a complete characterization on an optimal threshold policy, and implement the characterized optimal policy in realistic settings with random renewable generation and electricity prices. Numerical results demonstrate that the value of storage (the consumer's net benefit obtained by optimally operating the storage) increases with the generation from renewable sources.

Keywords:Networked control systems Abstract: As intelligent automation and large-scale distributed monitoring and control systems become more widespread, concerns are growing about the way these systems collect and make use of privacy-sensitive data obtained from individuals. This tutorial paper gives a systems and control perspective on the topic of privacy preserving data analysis, with a particular emphasis on the processing of dynamic data as well as data exchanged in networks. Specifically, we consider mechanisms enforcing differential privacy, a state-of-the-art definition of privacy initially introduced to analyze large, static datasets, and whose guarantees hold against adversaries with arbitrary side information. We discuss in particular how to perform tasks such as signal estimation, consensus and distributed optimization between multiple agents under differential privacy constraints.

Keywords:Networked control systems, Cooperative control, Hybrid systems Abstract: In this paper, we consider the distributed consensus problem of the second-order multi-agent system where the agents are connected via distance-dependent networks. For the feasibility of information processing, we introduce dwell times which may be different at different sampling time instants. Each agent can only receive the information and update its control laws at discrete sampling time instants, which in combination with the continuous-time dynamics yields the hybrid closed-loop dynamics. By analyzing the discrete-time system at the sampling instants and the continuous-time system between the sampling instants, we establish the sufficient condition for consensus of the hybrid second-order multi-agents system, without relying on the properties of the dynamics of the neighbor graphs.

Keywords:Networked control systems, Decentralized control, Lyapunov methods Abstract: In this paper we focus on practical feedback stabilization strategies for dissipative systems. We design control strategies that are sparse, in the sense that they require a minimal number of active components. The result applies to multi-agent systems and it allows consensus arising via external intervention.

Keywords:Networked control systems, Distributed control, Decentralized control Abstract: We consider the distributed average tracking problem where a group of agents estimates the global average of bandlimited signals using only local communication. An estimator is designed to solve this problem with minimal error. Previous discrete-time designs are limited to tracking signals which either are constant, are slowly varying, have a known model (or frequency), or consist of a single unknown frequency which can be estimated. In contrast, we propose a feedforward design which is capable of tracking the average of arbitrary bandlimited signals. The communication graph is assumed to be connected and symmetric with non-zero weighted Laplacian eigenvalues in a known interval, although simulations show that the performance degrades gracefully as these assumptions are violated. Our design also provides the estimate of the average without delay and is robust to changes in graph topology.

Keywords:Networked control systems, Distributed control, Smart grid Abstract: This paper considers the power sharing problem for a grid-connected AC microgrid consisting of multiple dispatchable distributed generators. The microgrid is modeled as a multi-agent system and the power sharing problem is formulated as an interconnected leader-following consensus problem in the sense that the leader is affected by the followers passively. To solve this interconnected leader-following consensus problem, a distributed control scheme is proposed. First, each distributed generator is equipped with a distributed observer to communicate with each other and agree on a global reference signal, based on which the local reference power output is determined in proportion to its power capacity. Second, local tracking controller is designed for each distributed generator to achieve local reference power output tracking. It is proven that, under this control scheme, power sharing among all the distributed generators can be accomplished autonomously. Simulation results are presented to validate the effectiveness of the proposed control scheme.

Keywords:Distributed parameter systems, Networked control systems, Process Control Abstract: This work presents a methodology for the design and analysis of an output feedback-based event-triggered networked control system for spatially-distributed processes with uncertain low-order dynamics, a finite number of spatially-distributed output measurements and sensor-controller communication constraints. Based on an approximate finite-dimensional system that captures the infinite-dimensional system's dominant dynamics, a model-based controller is initially designed and implemented. A state observer, with well-characterized state estimation error convergence properties, is also designed and embedded in the sensor to estimate the slow states of the infinite-dimensional system based on the available output measurements. The observer state is used to update the model state at times when sensor-controller communication is permitted. The update is triggered whenever a certain stability threshold on the model estimation error is breached. The threshold is explicitly characterized in terms of the controller and observer design parameters, the model uncertainty and the control actuator and measurement sensor locations. The connections between the developed output-feedback-based event-triggered control approach and the full-state feedback-based strategy are identified and discussed. Finally, the proposed methodology is illustrated using a simulation example.

Keywords:Cooperative control, Distributed control, Networked control systems Abstract: The problem of connectivity assessment of an asymmetric network represented by a weighted directed graph is investigated in this paper. The notion of generalized algebraic connectivity is formulated for this type of network in the context of distributed parameter estimation algorithms. The proposed connectivity measure is then defined in terms of the eigenvalues of the Laplacian matrix of the graph representing the network. A novel distributed algorithm based on the subspace consensus approach is developed to compute the generalized algebraic connectivity from the viewpoint of each node. The Laplacian matrix of the network is properly transformed such that the problem of finding the connectivity measure is reduced to the problem of finding the dominant eigenvalue of an asymmetric matrix. Two sequences of one-dimensional and two-dimensional subspaces are generated iteratively by each node such that either of them converges to the desired subspace spanned by the eigenvectors associated with the desired eigenvalues representing the network connectivity. The effectiveness of the distributed algorithm is subsequently demonstrated by simulations.

Keywords:Cooperative control, Sensor fusion Abstract: This paper focuses on the study of consensus-based information fusion for a team of sensors, where some of them are active, in directed networks when communication among sensors is directed. In the context of this paper, a sensor is called active if it can obtain information about certain objects while a sensor is called inactive if it cannot obtain information. Moreover, each sensor is able to determine if it is active or inactive. Although inactive sensors do not provide information, they are needed in order to maintain connectivity of the communication graph. Due to the existence of inactive sensors, the existing research on consensus-based information fusion for a team of active sensors cannot be applied. We first provide a mathematical formulation of consensus-based information fusion for both inactive and active sensors. Then we derive sufficient conditions to guarantee that all active and inactive sensors reach consensus on their final state information. In particular, we consider two different cases: (1) the existence of one inactive sensor, and (2) the existence of multiple inactive sensors. For the first case, we also show explicitly the final state information of all active sensors.

Keywords:Optimization, Optimization algorithms, Networked control systems Abstract: This paper introduces saddle-point methods for distributed continuous-time online convex optimization, where the system objective function varies arbitrarily over time subject to some global inequality constraints. The overall dynamics of the proposed saddle-point controller are described by a system of differential equations, coupled linearly through the network Laplacian. The controller pushes actions along the negative gradient direction of the objective, constraint violation, as well as network disagreement using only causal and locally available information, while dynamically adapting the Lagrange multipliers in a decentralized fashion. We define regret as the cost difference with the optimal action over time. We show that the proposed saddle-point controller achieves a regret of order O(sqrt{T}) with the time horizon T. We also address the impact of the network topology, encoded in the spectrum of the network Laplacian, as a factor on the speed of convergence.

Keywords:Agents-based systems, Cooperative control, Aerospace Abstract: This paper studies the problem of localising a Global Positioning System (GPS)-denied Unmanned Aerial Vehicle (UAV) in two-dimensional space. Suppose there are two vehicles, one which is equipped with GPS and the other is GPS-denied (but has an inertial navigation system (INS) and so is able to determine its trajectory in a local coordinate frame, but not a global coordinate frame). The GPS-equipped vehicle broadcasts its global coordinates to the GPS-denied vehicle and the GPS-denied vehicle also obtains, in its local coordinate frame, a bearing measurement of the GPS-equipped UAV. The paper shows that with four or more such measurements and generic trajectories of the two UAVs, localisation in a global coordinate frame of the GPS-denied UAV is achievable. Certain nongeneric trajectories for which localisation is impossible are also identified. While in the first instance, the solution assumes zero noise in the measurements, the techniques are then extended to deal with the presence of measurement noise.

Keywords:Distributed parameter systems, Sensor networks, Kalman filtering Abstract: This paper presents a cooperative filtering scheme for online parameter identification of 2D diffusion processes using data collected by a mobile sensor network moving in the diffusion field. The diffusion equation is incorporated into the information dynamics associated with the trajectories of the mobile sensors. A cooperative Kalman filter is developed to provide estimates of field values, the gradient, and the temporal variations of the field values along the trajectories. This leads to a co-design scheme for state estimation and parameter identification for diffusion processes that is different from using static sensors. Utilizing the state estimates from the filters, a recursive least square (RLS) algorithm is designed to estimate the unknown diffusion coefficient of the field. A set of sufficient conditions is derived for the convergence of the cooperative Kalman filter. Simulation results show satisfactory performance of the proposed method

Keywords:Biologically-inspired methods, Agents-based systems, Distributed control Abstract: A novel bio-inspired strategy, the Hybrid Speeding Up Slowing Down (Hybrid SUSD) strategy, is introduced to achieve distributed control of a multi-agent system for the localization of multiple sources in a search space. Hybrid SUSD switches between bio-inspired exploration algorithms and exploitation algorithms. The exploration algorithms provide coverage of the workspace with non-zero probability. The exploitation algorithms leverage the SUSD strategy for source seeking without explicit gradient estimation. Conditions for switching between exploration and exploitation are developed based on measurements taken by an agent and the number of neighbors an agent may have. Given a confined search space, the convergence of the hybrid SUSD to locate all sources is rigorously justified. Simulation results confirm that the strategy allows each agent to converge to one of the source locations. The Hybrid SUSD may be used as a distributed optimization algorithm that is able to find all minima of a function over a confined search space.

Keywords:Cooperative control, Multivehicle systems, Optimal control Abstract: This paper considers a distributed system of identical agents with arbitrary LTI models. A method for distributed state-feedback design is provided. The proposed solution consists of two steps: first a single-agent controller is derived and then, based on the network topology, the gain of this controller is adjusted. LQ optimality of this controller is proved provided that the Laplacian has only real eigenvalues and is non-defective. The result is subsequently used to design a controller for asymmetric vehicle platoon. We show that the same controller with a fixed gain is the optimal controller for any number of vehicles in the platoon. However, the performance of the optimal controller is still subject to inherent limitations given by the network topology. In some cases, even exponential scaling in the number of vehicles must occur for any controller.

Keywords:Network analysis and control, Control of networks, Networked control systems Abstract: Controllability analysis of a network through its topology has recently been a popular issue in the systems and control community. In this regard, the zero extension rule is introduced in this paper, which provides a sufficient number of control nodes to ensure the controllability of certain families of undirected networks through the notion of their balancing sets. Moreover, some lower bounds on the dimension of the controllable subspace are provided. Finally, based on the generalized zero extension rule, some controllability conditions for such special structure of networks as the path, cycle, and three-branch tree are derived.

Keywords:Control of networks, Constrained control, Robotics Abstract: This paper presents a strategy for the position control of mobile robotic networks subject to geometric constraints. The main idea of this paper is to show that passivity arguments can be used to ensure both stability and constraints satisfaction. It is shown that it is possible to pre-stabilize the system dynamics with a proportional-integral consensus estimator and a proportional feedback loop which make use of passivity arguments. Then, the very same passivity arguments are used to ensure constraints satisfaction, using a set-invariance based Reference Governor. Simulations and experiments are carried out to demonstrate the effectiveness of the proposed solution.

Keywords:Control of networks, Cooperative control, Robotics Abstract: Teleoperating Cyber-Physical System (TCPS) is referred as a promising technology to extend human actions and intelligences to remote locations. The task of how to collaborate master operator and slaves to keep a desired formation is largely unexplored. This paper is concerned with a formation control problem for multi-slave TCPS, subjected to time-varying delay in cyber channels and actuator saturation in physical channels. We first design a controller to enforce the formation of master and slave robots. Sufficient conditions for stability are provided to show that the formation controller can stabilize the TCPS in the presence of time delay and actuator saturation constrains. Finally, simulations are performed to validate our proposed results. It is demonstrated that the formation controller can guarantee global asymmetric stability of TCPS if the required conditions are satisfied.

Keywords:Control of networks, Distributed control, Networked control systems Abstract: This paper addresses the problem of asymptotical frequency synchronization and phase-difference tracking for Kuramoto oscillators with N distinct natural frequencies. Through the stability analysis of Kuramoto oscillators with distributed phase-difference tracking controllers, we discover that by controlling phase-difference tracking errors and their integrations, the individual frequencies can asymptotically synchronize to the average natural frequencies of the group and phase differences can asymptotically track the given references. We also extend the proposed phase-difference tracking control to islanded microgrids assuming there are local controllers maintaining the voltage stability, to achieve frequency synchronization and control angle differences of voltages. Simulations, including the numerical examples of a network of N = 4 Kuramoto oscillators and an islanded microgrid consisting of two frequency-droop controllers and two loads, are provided to verify the effectiveness of proposed control strategies.

Keywords:Control of networks, Energy systems, Lyapunov methods Abstract: A differential-algebraic nonlinear dynamic model for FFNs with multiple fan branches is proposed based on the branch dynamics and network graph properties. Then, a novel adaptive decentralized flowrate-pressure controller, which takes a proportional-integral (PI) form, is established. This controller not only guarantees the satisfactory closed-loop stability but also has no need in the values of network physical parameters. This newly-built adaptive control is then applied to solve the flowrate-pressure regulation problem for the secondary loop of an under-constructed two-modular high temperature gas-cooled nuclear plant, and the numerical simulation results show the feasibility and high performance of this network control strategy.

Keywords:Control of networks, Linear systems Abstract: This paper studies the synchronization properties of networks of identical, linear time-invariant systems. It is shown that networks of passive systems synchronize for any directed and rooted communication topology, thus generalizing a well known result on synchronization in networks of single integrators. If the passivity property is relaxed to output-feedback-passivity, synchronization is proven for arbitrarily large subsets of directed and rooted communication graphs, by imposing a sufficiently high feedback gain. Finally, it is shown that, in networks of single-input single-output systems, passivity is not only sufficient but it is also, to a certain extent, necessary for the above property to hold.

Keywords:Delay systems, Communication networks, PID control Abstract: This paper addresses the stabilization problem of delay models of Transmission Control Protocol/Active Queue Management (TCP/AQM) by using a Proportional- Derivative (PD) controller as AQM strategy. The complete set of PD controllers that exponentially stabilizes the linearization is determined in counterpart with the existing works in the literature which only give an estimate of it. Additionally, a simple procedure for determining a non-fragile PD controller that admits controller coefficient perturbations is provided.

Keywords:Large-scale systems, Communication networks, Stability of hybrid systems Abstract: In this paper we consider systems consisting of a number of spatially invariant, i.e., identical, subsystems that use packet-based communication networks for the exchange of information. Recent literature has shown that for an infinite number of such interconnected networked subsystems, the overall system can be modeled as an infinite interconnection of identical hybrid (sub)systems. Based on this hybrid modeling perspective, conditions were derived guaranteeing uniform global exponentially stability (UGES) or Lp-gain performance. These conditions were formulated locally in the sense that only the local dynamics of a single hybrid subsystem in the interconnection is needed in order to obtain a maximally allowable transmission interval (MATI) for all of the individual communication networks such that these global stability properties are guaranteed for the complete infinite-dimensional system. In this work we will connect these results to other known results in the literature concerning infinite-dimensional spatially invariant systems and extend them in various directions, thereby showing the generic nature of the obtained hybrid modeling framework. In particular, it is shown that the stability and performance conditions as derived for the perfect communication case of the infinite spatially invariant interconnection guarantee robustness of the stability/performance property in the packet-based communication case. In addition, extensions to periodic interconnections and finite interconnections with boundary conditions will be discussed explicitly, bringing the theory closer to practical applications, which will be epitomized in a two-sided vehicular platooning example concerning L2-stability.

Keywords:Communication networks, Machine learning Abstract: In this paper we provide a distributed and asynchronous implementation of the C-means data clustering algorithm to let the agents in a sensor network partition themselves based on the observations available at each node (e.g., sensor data, positions, etc.) and to identify a small set of values which are representative of the observations. The clusters thus obtained are not mutually exclusive, in that each node is allowed to belong with different intensity to the different clusters. The proposed approach amounts to repeated depth-first visits of the network and imposes low requirements on memory, communication bandwidth and algorithmic complexity.

Keywords:Communication networks, Network analysis and control Abstract: This paper applies stochastic network calculus (SNC) to window ﬂow controllers. These controllers limit the arrivals to a protected part of the queuing system. Although deterministic network calculus (DNC) provides a worst-case analysis, a probabilistic extension has been unavailable so far. This paper presents two methods to treat window ﬂow controlled systems within SNC: The ﬁrst is a topological change to enforce a subadditive feedback loop. The second method, instead, bounds the probability to not have a subadditive feedback loop. A numerical example demonstrates how both methods signiﬁcantly improve the deterministic results.

Keywords:Communication networks, Randomized algorithms, Stochastic optimal control Abstract: In this paper, we consider optimal distributed scheduling of real-time traffic with hard deadlines in an ad hoc wireless network. Specifically, we assume the links share a common wireless channel and interference is represented by a conflict graph. Periodic single-hop traffic is considered where packets arrive at the beginning of each frame and need to be delivered by the end of the frame (otherwise, packets will be dropped). Each link is required to guarantee a maximum allowable packet dropping rate. We show that the real-time scheduling problem is combinatorial and tends to be intractable as the network size increases. To solve the real-time scheduling problem, we propose a frame-based carrier-sense multiple access (CSMA) algorithm which is shown to be asymptotically optimal. Moreover, it can be implemented in a distributed manner with low complexity. Simulation results also demonstrate the ability of our algorithm to meet the QoS requirements on deadlines.

Keywords:Communication networks, Sensor networks, Discrete event systems Abstract: The Cholesky decomposition represents a fundamental building block in order to solve several matrix-related problems, ranging from matrix inversion to determinant calculation, and it finds application in several contexts, e.g., in Unscented Kalman Filters or other least-square estimation problems. In this paper we develop a distributed algorithm for performing the Cholesky decomposition of a sparse matrix. We model a network of n agents as a connected undirected graph, and we consider a symmetric positive definite n x n matrix M with the same structure as the graph (i.e., except for the diagonal entries, nonzero coefficients m_{ij} are allowed only if there is a link between the i-th and the j-th agent). We develop an asynchronous and distributed algorithm to let each agent i calculate the nonzero coefficients in the i-th column of the Cholesky decomposition of M. With respect to the state of the art, the proposed algorithm does not require orchestrators and finds application in sparse networks with limited bandwidth and memory requirements at each node.

Keywords:Game theory, Machine learning, Pattern recognition and classification Abstract: Decision making in modern large-scale and complex systems such as communication networks, smart electricity grids, and cyber-physical systems motivate novel game-theoretic approaches. This paper investigates big strategic (non-cooperative) games where a finite number of individual players each have a large number of continuous decision variables and input data points. Such high-dimensional decision spaces and big data sets lead to computational challenges, relating to efforts in non-linear optimization scaling up to large systems of variables. In addition to these computational challenges, real-world players often have limited information about their preference parameters due to the prohibitive cost of identifying them or due to operating in dynamic online settings. The challenge of limited information is exacerbated in high dimensions and big data sets. Motivated by both computational and information limitations that constrain the direct solution of big strategic games, our investigation centers around reductions using linear transformations such as random projection methods and their effect on Nash equilibrium solutions. Specific analytical results are presented for quadratic games and approximations. In addition, an adversarial learning game is presented where random projection and sampling schemes are investigated.

Keywords:Game theory Abstract: We study diffusion of cooperation in a two-population game in continuous time. At each instant, the game involves two random individuals, one from each population. The game has the structure of a Prisoner’s dilemma where each player can choose either to cooperate (c) or to defect (d), and is reframed within the field of approachability in two-player repeated game with vector payoffs. We turn the game into a dynamical system, which is positive, and propose a saturated strategy that ensures local asymptotic stability of the equilibrium (c, c) for any possible choice of the payoff matrix. We show that there exists a rectangle, in the space of payoffs, which is positively invariant for the system. We also prove that there exists a region in the space of payoffs for which the equilibrium solution (d, d) is an attractor, while all of the trajectories originating outside that region, but still in the positive quadrant, are ultimately bounded in the rectangle and, under suitable assumptions, converge to the solution (c, c).

Keywords:Game theory, Mean field games, Communication networks Abstract: In this paper we develop a novel approach to the convergence of Best-Response Dynamics for the family of interference games. In contrast to congestion games, interference games are generally not potential games. Therefore, proving the convergence of the best-response dynamics to a Nash equilibrium in these games requires new techniques. We suggest a model for random interference games, based on channel gains which are dictated by the random locations of the players. Our goal is to prove convergence of approximate best-response dynamics with high probability with respect to the randomized game. We embrace the asynchronous model in which the acting player is chosen at each stage at random. In our approximate best-response dynamics, the action of a deviating player is chosen at random among all the approximately best ones. We show that with high probability, asymptotically with the number of players, each action increases the expected social-welfare (sum of achievable rates). Hence, the induced sum-rate process is a submartingale. Based on the Martingale Convergence Theorem, we prove convergence of the strategy profile to an approximate Nash equilibrium with good performance for asymptotically almost all interference games. Finally, we demonstrate our results in simulated examples.

Keywords:Game theory, Distributed control, Network analysis and control Abstract: In this paper, we consider a resource allocation game with binary preferences and limited capacities over large scale networks and propose a novel randomized algorithm for searching its pure-strategy Nash equilibrium points. It is known that such games always admit a pure-strategy Nash equilibrium and benefit from having a low price of anarchy. However, the best known theoretical results only provide a quasi-polynomial constant approximation algorithm of the equilibrium points over general networks. Here, we search the state space of the resource allocation game for its equilibrium points. We use a random tree based search method to minimize a proper score function and direct the search toward the pure-strategy Nash equilibrium points of the system. We demonstrate efficiency of our algorithm through some empirical results.

Keywords:Game theory, Large-scale systems, Optimization algorithms Abstract: We consider the problem to control a large population of noncooperative heterogeneous agents, each with strongly convex cost function depending on the average population state and convex constraints, towards an aggregative Nash equilibrium. We assume a minimal information structure through which a central controller can broadcast incentive signals to control the decentralized optimal responses of the agents. We propose a dynamic controller that, based on fixed point operator theory arguments, ensures global convergence if a sufficient condition on the matrix parameter defining the cost functions holds, yet independently on the convex constraints.

Keywords:Game theory, Distributed control, Network analysis and control Abstract: In this paper, we consider a reputation system, where a number of individuals express their opinions, modeled by discrete scalars in the interval [0,1], about an object and the object’s score (reputation) is determined as the arithmetic mean of all expressed opinions. An individual’s expressed opinion may or may not be consistent with her actual opinion, a continuous scalar in [0,1], for a variety of reasons. In this paper, we address in a unified, game-theoretic framework the influence of two opposing social behaviors, namely conformity and manipulation, on the outcome of a reputation system. For the purposes of this paper, conformity as a social behavior refers to the tendency of an individual to express an opinion that matches the public opinion, whereas manipulation refers to the tendency of an individual to express an opinion so as to manipulate the public opinion toward her actual opinion.

Keywords:Optimal control, Predictive control for linear systems, Optimization Abstract: Partial (or block) condensing is a recently proposed technique to reformulate a Model Predictive Control (MPC) problem into a form more suitable for structure-exploiting Quadratic Programming (QP) solvers. It trades off horizon length for input vector size, and this degree of freedom can be employed to find the best problem size for the QP solver at hand. This paper proposes a Hessian condensing algorithm particularly well suited for partial condensing, where a state component is retained as an optimization variable at each stage of the partially condensed MPC problem. The optimal input-horizon trade-off is investigated from a theoretical point of view (based on algorithms flop count) as well as by benchmarking (in practice, the performance of linear algebra routines for different matrix sizes plays a key role). Partial condensing can also be seen as a technique to replace many operations on small matrices with fewer operations on larger matrices, where linear algebra routines perform better. Therefore, in case of small-scale MPC problems, partial condensing can greatly improve performance beyond the flop count reduction.

Keywords:Optimal control, Robotics Abstract: Purcell’s swimmer is a classical model of a simple three-link swimmer moving in a highly viscous fluid, similar to the motion of microscopic organisms or robotic microswimmers. The two joint angles are commonly prescribed as periodic trajectories called gaits, so that the dynamics of Purcell’s swimmer can be formulated as a driftless nonlinear control system. In a famous paper by Tam and Hosoi, they have found the optimal gait that maximizes net displacement over a cycle by representing the time-periodic joint angles as truncated Fourier series and numerically optimizing a finite set of their coefficients. In this work, the gait optimization is revisited and analytically formulated as an elegant problem of optimal control system with only two state variables, which can be solved using Pontryagin’s maximum principle. Due to absence of any physical constraints on the control system’s input, it turns out that the optimal solution must follow a “singular arc”. Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi’s optimal gait

Keywords:Optimal control, Robust control, Algebraic/geometric methods Abstract: In this paper, a framework of nonlinear optimal control robust to parameter variation is considered. We evaluate the sensitivity of the system regarding the parameter variation by using a variational system. We clarify some properties such as local controllability of the variational system and provide remarks on the proposed framework. A numerical example shows the control performance of the proposed method.

Keywords:Optimal control, Stochastic systems, Mean field games Abstract: This paper is concerned with discrete-time mean-field linear-quadratic (LQ) control problem. A thorough solution to the problem is given for the first time. The sufficient and necessary condition for the solvability of mean-field LQ control problem is firstly presented in analytical expression based on the maximum principle developed in this paper, which is compared with the results obtained in literatures where only operator type solvability conditions were given. The optimal controller is given in terms of a coupled Riccati equation which is derived from the solution to forward and backward stochastic difference equation (FBSDE).

The key techniques adopted in this paper are the maximum principle and the solution to the FBSDE obtained in this paper. The derived results in this paper will provide us the insight to solve the mean-field control problem for continuous-time systems and other related problems.

Keywords:Optimal control Abstract: This paper is devoted to a study of a discrete time infinite horizon optimal control problem with time discounting criterion. We introduce an infinite-dimensional linear programming (IDLP) problem closely related to this problem. We derive necessary and sufficient conditions of optimality for the optimal control problem in terms of the solution of the dual to this IDLP problem.

Beihang Univ. (Beijing Univ. of Aeronautics and Astron

Keywords:Optimal control Abstract: In this paper, we consider a class of n-dimensional discrete-time bilinear systems which can be nearly controllable. We first show that, to achieve near-controllability, at least n+1 control inputs are required. That is, the minimum time to steer the class of systems between any given pair of states is no less than n+1 time steps. We then prove by applying the root locus theory that the systems can be nearly controllable with exactly n+1 control inputs only if a corresponding matrix has no Jordan block with dimension greater than two and, meanwhile, has no more than one Jordan block with dimension two in its Jordan canonical form. Finally, we give examples to demonstrate the results of this paper.

Keywords:Optimization algorithms, Stochastic systems, Large-scale systems Abstract: The total-variation (TV) regularizer is often used to promote the structured sparsity of a given real function over the vertices of a non-directed graph. Indeed, the proximity operator associated with TV regularizer promotes sparsity of the function discrete gradient. Although quite affordable in the special case of one-dimensional (1D) graphs, the computation of the proximity operator for general large scale graphs can be demanding. In this paper, we propose a stochastic algorithm for solving this problem over large graphs with a moderate iteration complexity. The algorithm consists in properly selecting random paths in the graph and computing 1D-proximity operators over these paths. Convergence of the algorithm is related to recent results on stochastic proximal point algorithms.

Keywords:Optimization algorithms, Machine learning Abstract: Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong convexity of the objective function. To our knowledge, no rate statements exist in the absence of this assumption. Motivated by this gap, we allow the objective function to be merely convex and develop a regularized SQN method. In this scheme, both the gradient mapping and the Hessian approximation are regularized at each iteration and updated alternatively. Unlike the classical regularization schemes, we allow the regularization parameter to be updated alteratively and decays to zero. Under suitable assumptions on the stepsize and regularization parameters, we show that the function value converges to its optimal value in both an almost sure and an expected-value sense. In each case, a set of regularization and steplength sequences is provided under which convergence may be guaranteed. Moreover, the rate of convergence is derived in terms of function value. Our empirical analysis on a binary classification problem shows that the proposed scheme performs well compared to both classical regularized SQN and stochastic approximation schemes.

Keywords:Optimization algorithms, Stochastic systems, Iterative learning control Abstract: Stochastic optimization typically are solved via stochastic iterative algorithms. Examples are stochastic gradient descent, and other first-order methods for stochastic optimization. In such algorithms, exact computation of the gradient of the objective function is generally not possible. Hence, empirical estimates are used instead. We view such algorithms as a linear dynamical system but with noisy non-linear feedback. We give a general framework for probabilistic stability analysis of such dynamical systems. This is done via a novel stochastic dominance argument that was developed for convergence analysis of iterated random operators. We are also able to give a non-asymptotic rate of convergence within this framework.

Keywords:Optimization algorithms, Variational methods, Stochastic systems Abstract: Stochastic generalizations of the extragradient method are complicated by a key challenge: the scheme requires {em two} projections on a convex set and {em two evaluations} of the map for every major iteration. We consider two related avenues where every iteration requires a {em single projection}: (i) A projected reflected gradient (PRG) method requiring a {em single} evaluation of the map and a {em single} projection; and (ii) A modified backward-forward splitting (MBFS) method that requires {em two} evaluations of the map and a {em single projection}. We make the following contributions: (a) We prove almost sure convergence of the iterates to a random point in the solution set for the stochastic PRG scheme under a weak sharpness requirement; (b) We prove that the mean of the gap function associated with the averaged sequence diminishes to zero at the optimal rate of {cal O}(1/sqrt{N}) for both schemes where N is the iteration index.

Keywords:Stochastic optimal control, Iterative learning control, Optimization algorithms Abstract: We consider the online solution of discounted Markov decision processes (MDPs). We focus on the black-box learning model where transition probabilities and state transition cost are unknown. Instead, a simulator is available to generate random state transitions under given actions. We propose a stochastic primal-dual algorithm for solving the linear formulation of the Bellman equation. The algorithm updates the primal and dual iterates by using sample state transitions and sample costs generated by the simulator. We provide a thresholding procedure that recovers the exact optimal policy from the dual iterates with high probability. A numerical example is provided to verify the results.

Keywords:Time-varying systems, Optimization algorithms, Adaptive control Abstract: The stochastic gradient (SG) method has been widely applied in unconstrained stochastic optimization, and is particularly useful in sequential processing such as online learning. Core SG theories on convergence and asymptotic normality are developed on the basis of a stationary and unique optimizer. However, many real-world applications are often nonstationary in nature. In dynamic control systems and other time-varying problems, the true target parameter and/or the true loss function may drift over time, so there is no convergence per se. When drift occurs, SG with constant gain is often used to keep up with the nonstationary target. Several existing works on the tracking capability of recursive algorithms with a constant gain provide asymptotic stochastic big-O bounds of the tracking error. There are also some finite-iteration error bounds developed under fairly strong assumptions. In contrast, this paper builds a computable tracking error bound for SG, which is useful in both the finite-sample performance and the asymptotic analysis. The case of interest requires the strong convexity of the timevarying loss function, but with a mild restriction imposed on the drift associated with the nonstationary evolution. Our result complements existing big-O bound, and delivers a computable bound for practical use.

Keywords:Mean field games, Stochastic optimal control, Stochastic systems Abstract: This paper considers the modeling and analysis of continuous time stochastic growth optimization in a mean field game setting. The individual capital stock evolution is determined by production, consumption and stochastic depreciation. We adopt a Cobb-Douglas production function and HARA utility combining own consumption and relative consumption with respect to the population average. The use of relative consumption reflects human psychology of satisfaction, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the ratio type interaction in the utility structure, our performance estimate depends on large deviation techniques.

Keywords:Mean field games Abstract: Here, we consider one-dimensional first-order stationary mean-field games with congestion. These games arise when crowds face difficulty moving in high-density regions. We look at both monotone decreasing and increasing interactions and construct explicit solutions using the current formulation. We observe new phenomena such as discontinuities, unhappiness traps and the non-existence of solutions.

Keywords:Stochastic systems, Differential-algebraic systems, Systems biology Abstract: For the class of Ito-type nonlinear Stochastic Differential Equations (SDE), where the drift and the diffusion are σπ-functions (σπ-SDE), we prove that the (infinite) set of all moments of the solution satisfies a system of infinite ordinary differential equations (ODEs), which is always linear. The result is proven by showing first that a σπ-SDE can be cubified, i.e. reduced to a system of SDE of larger (but still finite) dimension in general, where drifts and diffusions are at most third-degree polynomial functions. Our motivation for deriving a moment equation in closed form comes from systems biology, where second-order moments are exploited to quantify the stochastic variability around the steady-state average amount of the molecular players involved in a bio-chemical reaction framework. Indeed, the proposed methodology allows to write the moment equations in the presence of non-polynomial nonlinarities, when exploiting the Chemical Langevin Equations (which are SDE) as a model abstraction. An example is given, associated to a protein-gene production model, where non- polynomial nonlinearities are known to occur.

Keywords:Stochastic systems, Optimization, LMIs Abstract: We propose convex controller synthesis algorithms for a class of stochastic differential equations (SDEs) with persistent noise. This includes SDEs in which the noise does not vanish at the equilibria of the system. Our performance criterion is Noise-to-State Stability (NSS) in the moments, which is a generalization of the input-to-state stability (ISS) for SDEs. We formulate synthesis algorithms that, in addition to guaranteeing asymptotic convergence in the case of zero input noise, ensure that an upper bound on the effect of input noise (defined by the Frobenius norm of the noise covariance) is minimized. In the case of linear SDEs, the algorithm is in terms of linear matrix inequalities and, in the case of polynomial data, the method is based on polynomial optimization. The method is illustrated by examples.

Univ. of New South Wales at the AustralianDefenceForceAcad

Keywords:Quantum information and control, Stochastic systems Abstract: The realization of transfer functions of Linear Quantum Stochastic Systems (LQSSs) is an issue of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. In this paper, we review two realization methods proposed by the authors in [1], [2], [3], [4]. The first one uses a cascade of a static linear quantum-optical network and single-mode optical cavities, while the second uses a feedback network of such cavities, along with static linear quantum-optical networks that pre- and post-process the cavity network inputs and outputs.

Keywords:Quantum information and control Abstract: We consider an open quantum system described by a Lindblad-type master equation with two time scales. The fast time scale is strongly dissipative and drives the system towards a low-dimensional decoherence-free space. To perform the adiabatic elimination of this fast relaxation, we propose a geometric asymptotic expansion based on the small positive parameter describing the time scale separation. This expansion exploits geometric singular perturbation theory and center-manifold techniques. We conjecture that, at any order, it provides an effective slow Lindblad master equation and a completely positive parameterization of the slow invariant sub-manifold associated to the low-dimensional decoherence-free space. By preserving complete positivity and trace, two important structural properties attached to open quantum dynamics, we obtain a reduced-order model that directly conveys a physical interpretation since it relies on effective Lindbladian descriptions of the slow evolution. At the first order, we derive simple formulae for the effective Lindblad master equation. For a specific type of fast dissipation, we show how any Hamiltonian perturbation yields Lindbladian second-order corrections to the first-order slow evolution governed by the Zeno-Hamiltonian. These results are illustrated on a composite system made of a strongly dissipative harmonic oscillator, the ancilla, weakly coupled to another quantum system.

Keywords:Machine learning, Biomedical, Pattern recognition and classification Abstract: We develop a new method for a particular type of a classification problem, where the positive class is a mixture of multiple clusters and the negative class is drawn from a single cluster. The new method employs an alternating optimization approach, which jointly discovers the clusters in the positive class, and at the same time, optimizes the classifiers that separate each positive cluster from the negative samples. The classifiers are designed under the Support Vector Machines (SVM) framework with double regularizations, and the whole alternating process is shown to converge. We compare this new method to the conventional SVM with a linear kernel or an RBF kernel and two other hierarchical classifiers which first cluster once and then classify. Experimental results with both simulated data and actual data demonstrate better prediction accuracy, as well as, successful cluster detection.

Keywords:Machine learning, Estimation Abstract: Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This opens the way to the application of efficient inference algorithms in the machine learning literature to solve the smoothing problem for reciprocal processes. Such algorithms are known to converge if the underlying graph is a tree. This is not the case for a reciprocal process, whose associated graphical model is a single loop network. The contribution of this paper is twofold. First, we introduce belief propagation for Gaussian reciprocal processes. Second, we establish a link between convergence analysis of belief propagation for Gaussian reciprocal processes and stability theory for differentially positive systems.

Keywords:Machine learning, Fluid flow systems, Markov processes Abstract: This paper formulates a class of partial differential equation (PDE) control problems as a reinforcement learning (RL) problem. We design an RL-based algorithm that directly works with the state of PDE, an infinite dimensional vector, thus allowing us to avoid the model order reduction, commonly used in the conventional PDE controller design approaches. We apply the method to the problem of flow control for time-varying 2D convection-diffusion PDE, as a simplified model for heating, ventilating, air conditioning (HVAC) control design in a room.

Keywords:Machine learning, Formal verification/synthesis, Automotive control Abstract: This paper uses active learning to solve the problem of mining signal temporal requirements of cyber-physical systems or simply the requirement mining problem. By utilizing robustness degree, we formulate the requirement mining problem as an optimization problem. We then propose a new active learning algorithm called Gaussian Process Adaptive Confidence Bound (GP-ACB) to help in solving the optimization problem. We show theoretically that the GP-ACB algorithm has a lower regret bound--thus a larger convergence rate--than some existing active learning algorithms, such as GP-UCB. We finally illustrate and apply our requirement mining algorithm with two case studies: the Ackley's function and a real world automotive power steering model. Our results demonstrate that there is a principled and efficient way of extracting requirements for complex cyber-physical systems.

Keywords:Machine learning, Kalman filtering, Learning Abstract: In this work we study the problem of efficient non-parametric estimation for non-linear time-space dynamic Gaussian processes (GP). We propose a systematic and explicit procedure to address this problem by pairing GP regression with Kalman Filtering. Under a specific separability assumption of the modeling kernel and periodic sampling on a (possibly non-uniform) space-grid, we show how to build an exact finite dimensional discrete-time state-space representation for the modeled process. The major finding is that the state at instant k of the associated Kalman Filter represents a sufficient statistic to compute the minimum variance prediction of the process at instant k over any arbitrary finite subset of the space. Finally, we compare the proposed strategy with standard approaches.

Keywords:Machine learning, Subspace methods Abstract: We describe a test statistic based on the L^1-norm of the eigenvectors of a modularity matrix to detect the presence of an embedded Erdos-Renyi (ER) subgraph inside a larger ER random graph. We make use of the properties of the asymptotic distribution of eigenvectors of random graphs to derive the distribution of the test statistic under certain conditions on the subgraph size and edge probabilities. We show that the distributions differ sufficiently for well defined ranges of subgraph sizes and edge probabilities of the background graph and the subgraph. This method can have applications where it is sufficient to know whether there is an anomaly in a given graph without the need to infer its location. The results we derive on the distribution of the components of the eigenvector may also be useful to detect the subgraph nodes.

Keywords:Closed-loop identification, Identification Abstract: When identifying all modules in a dynamic network it is natural to treat all node variables in a symmetric way, i.e. not having pre-assigned roles of 'inputs' and 'outputs'. In a prediction error setting this implies that every node signal is predicted on the basis of all other nodes. A usual restriction in direct and joint-io methods for dynamic network and closed-loop identification is the need for a delay to be present in every loop (absence of algebraic loops) . It is shown that the classical one-step-ahead predictor that incorporates direct feedthrough terms in models can not be used in a dynamic network setting. It has to be replaced by a network predictor, for which consistency results are shown when applied in a direct identification method. The result is a one-stage direct/joint-io method that can handle the presence of algebraic loops. It is illustrated that the identified models have improved variance properties over instrumental variable estimation methods.

Keywords:Identification, Closed-loop identification Abstract: We address the problem of identifying a specific module in a dynamic network, assuming known topology. We express the dynamics by an acyclic network composed of two blocks where the first block accounts for the relation between the known reference signals and the input to the target module, while the second block contains the target module. Using an empirical Bayes approach, we model the first block as a Gaussian vector with covariance matrix (kernel) given by the recently introduced stable spline kernel. The parameters of the target module are estimated by solving a marginal likelihood problem with a novel iterative scheme based on the Expectation-Maximization algorithm. Numerical experiments illustrate the effectiveness of the proposed method.

Keywords:Stochastic systems, Identification Abstract: In many application scenarios the underlying structure of a distributed system is described by using a graph representing the influence among its individual components. Indeed, given an unknown complex system, deriving information about its connectivity structure is often the first step to understand its fundamental mechanisms. There are several techniques in the scientific literature to infer influence diagrams for networks of dynamic systems, however, most of them can not deal with the presence of latent (unmeasured) components. The article provides sufficient conditions for reconstruction of networks of dynamic systems with polytree structure in the presence of latent nodes. No a priori assumptions are made about the location and number of hidden nodes.

Keywords:Networked control systems, Identification, Optimization Abstract: We study the problem of identifying sparse interaction topology using sample covariance matrix of the state of the network. Specifically, we assume that the statistics are generated by a stochastically-forced undirected first-order consensus network with unknown topology. We propose a method for identifying the topology using a regularized Gaussian maximum likelihood framework where the l1 regularizer is introduced as a means for inducing sparse network topology. The proposed algorithm employs a sequential quadratic approximation in which the Newton's direction is obtained using coordinate descent method. We provide several examples to demonstrate good practical performance of the method.

Keywords:Identification, Large-scale systems Abstract: Positive systems frequently appear in applications, and enjoy substantially simplified analysis and control design compared to the general LTI case. In this paper we construct a polytopic parameterization of all stable positive systems, and a convex upper bound for simulation error (a.k.a. output error) for which the resulting optimization is a linear program. Previous work on analogous methods for both the positive and general LTI case result in semidefinite programs. We exploit the decomposability of the constraints in these linear programs to develop distributed solutions applicable to identification of large-scale networked systems.

Keywords:Identification, Machine learning Abstract: This paper is concerned with the input design for Kernel-Based system identification methods. It proposes a method for input design which maximizes the information obtained through experiment based on a prior information on the target systems. The mutual information is adopted as such an information measure, and its closed form expression is obtained in terms of the kernel matrix, which expresses a prior information of the target system. The effectiveness of the proposed method is demonstrated through a numerical example.

Keywords:Iterative learning control, Multivehicle systems, Robotics Abstract: The goal of this work is to enable a team of quadrotors to learn how to accurately track a desired trajectory while holding a given formation. We solve this problem in a distributed manner, where each vehicle has only access to the information of its neighbors. The desired trajectory is only available to one (or few) vehicles. We present a distributed iterative learning control (ILC) approach where each vehicle learns from the experience of its own and its neighbors’ previous task repetitions, and adapts its feedforward input to improve performance. Existing algorithms are extended in theory to make them more applicable to real-world experiments. In particular, we prove stability for any causal learning function with gains chosen according to a simple scalar condition. Previous proofs were restricted to a specific learning function that only depends on the tracking error derivative (D-type ILC). Our extension provides more degrees of freedom in the ILC design and, as a result, better performance can be achieved. We also show that stability is not affected by a linear dynamic coupling between neighbors. This allows us to use an additional consensus feedback controller to compensate for non-repetitive disturbances. Experiments with two quadrotors attest the effectiveness of the proposed distributed multi-agent ILC approach. This is the first work to show distributed ILC in experiment.

Keywords:Identification, Machine learning, Linear systems Abstract: The stable spline kernel and the diagonal correlated kernel are two kernels that have been tested extensively in kernel-based regularization methods for LTI system identification. As shown in our recent works, although these two kernels are introduced in different ways, they share some common features, e.g., they all belong to the class of exponentially convex locally stationary kernels, and state-space model induced kernels. In this work, we further show that similar to the derivation of the stable spline kernel, the continuous-time diagonal correlated kernel can be derived by applying the same ``stable'' coordinate change to a ``generalized'' first order spline kernel, and thus can be interpreted as a stable generalized first order spline kernel. This interpretation provides new facets to understand the properties of the diagonal correlated kernel. Due to this interpretation, new eigendecompositions, explicit expression of the norm, and new maximum entropy interpretation of the diagonal correlated kernel are derived accordingly.

Keywords:Learning, Robotics, Optimal control Abstract: Traditional learning approaches proposed for controlling quadrotors or helicopters have focused on improving performance for specific trajectories by iteratively improving upon a nominal controller, for example learning from demonstrations, iterative learning, and reinforcement learning. In these schemes, however, it is not clear how the information gathered from the training trajectories can be used to synthesize controllers for more general trajectories. Recently, the efficacy of deep learning in inferring helicopter dynamics has been shown. Motivated by the generalization capability of deep learning, this paper investigates whether a neural network based dynamics model can be employed to synthesize control for trajectories different than those used for training. To test this, we learn a quadrotor dynamics model using only translational and only rotational training trajectories, each of which can be controlled independently, and then use it to simultaneously control the yaw and position of a quadrotor, which is non-trivial because of nonlinear couplings between the two motions. We validate our approach in experiments on a quadrotor testbed.

Keywords:Machine learning, Stability of nonlinear systems Abstract: Control theory can provide useful insights into the properties of controlled, dynamic systems. One important property of nonlinear systems is the region of attraction (ROA), a safe subset of the state space in which a given controller renders an equilibrium point asymptotically stable. The ROA is typically estimated based on a model of the system. However, since models are only an approximation of the real world, the resulting estimated safe region can contain states outside the ROA of the real system. This is not acceptable in safety-critical applications. In this paper, we consider an approach that learns the ROA from experiments on a real system, without ever leaving the true ROA and, thus, without risking safety-critical failures. Based on regularity assumptions on the model errors in terms of a Gaussian process prior, we use an underlying Lyapunov function in order to determine a region in which an equilibrium point is asymptotically stable with high probability. Moreover, we provide an algorithm to actively and safely explore the state space in order to expand the ROA estimate. We demonstrate the effectiveness of this method in simulation.

Keywords:Neural networks, Learning, Mechanical systems/robotics Abstract: Deep Neural Networks (DNNs) can be used as function approximators in Reinforcement Learning (RL). One advantage of DNNs is that they can cope with large input dimensions. Instead of relying on feature engineering to lower the input dimension, DNNs can extract the features from raw observations. The drawback of this end-to-end learning is that it usually requires a large amount of data, which for realworld control applications is not always available. In this paper, a new algorithm, Model Learning Deep Deterministic Policy Gradient (ML-DDPG), is proposed that combines RL with state representation learning, i.e., learning a mapping from an input vector to a state before solving the RL task. The ML-DDPG algorithm uses a concept we call predictive priors to learn a model network which is subsequently used to pre-train the first layer of the actor and critic networks. Simulation results show that the ML-DDPG can learn reasonable continuous control policies from high-dimensional observations that contain task-irrelevant information. Furthermore, in some cases, this approach significantly improves the final performance in comparison to end-to-end learning.

Keywords:Machine learning, Statistical learning, Identification Abstract: We propose a modified expectation-maximization algorithm by introducing the concept of quantum annealing, which we call the deterministic quantum annealing expectation-maximization algorithm (DQAEM). The expectation-maximization algorithm (EM) is an established algorithm to compute maximum likelihood estimates and applied to many practical applications. However, it is known that EM heavily depends on initial values and its estimates are sometimes trapped by local optima. To solve such a problem, quantum annealing (QA) was proposed as a novel optimization approach motivated by quantum mechanics. By employing QA, we then formulate DQAEM and present a theorem that supports its stability. Finally, we demonstrate numerical simulations to confirm its efficiency.

Keywords:Algebraic/geometric methods, Model/Controller reduction, Biological systems Abstract: We exploit a novel geometric method to construct the global isochrones of relaxation oscillators and the associated phase response curve. This method complements the classical infinitesimal (local) phase response curve approach by constructively predicting the finite phase-response curve near the singular limit of infinite timescale separations between the oscillator variables. We illustrate the power of our construction on the FitzHugh-Nagumo model of neuronal spike generation. Because of its global and constructive nature, not requiring extensive numerical simulations, the proposed approach is particularly suited to control design applications.

Keywords:Algebraic/geometric methods, Network analysis and control, Modeling Abstract: Negative imaginary and counter-clockwise systems have attracted attention as an interesting class of systems, which is well-motivated by applications. In this paper first the formulation and extension of negative imaginary and counter-clockwise systems as (nonlinear) input-output Hamiltonian systems with dissipation is summarized. Next it is shown how by considering the time-derivative of the outputs a port-Hamiltonian system is obtained, and how this leads to the consideration of alternate passive outputs for port-Hamiltonian systems. Furthermore, a converse result to positive feedback interconnection of input-output Hamiltonian systems with dissipation is obtained, stating that the positive feedback interconnection of two linear systems is an input-output Hamiltonian system with dissipation if and only if the systems themselves are input-output Hamiltonian systems with dissipation. This implies that the Poisson and resistive structure matrices can be redefined in such a way that the interaction between the two systems only takes place via the coupling term in the Hamiltonian of the interconnected system. Subsequently, it is shown how the positive feedback interconnection of two nonlinear input-output Hamiltonian systems with dissipation can be extended to the network interconnection of such systems, and how this leads to a stability analysis of the interconnected system in terms of the Hamiltonians and output mappings of the component systems associated to the vertices, as well as of the network topology.

Keywords:Algebraic/geometric methods, Nonholonomic systems, Computational methods Abstract: In a continuous-time nonlinear driftless control system, a geometric phase is a consequence of nonintegrability of the vector fields, and it describes how cyclic trajectories in shape space induce non-periodic motion in phase space, according to an area rule. The aim of this paper is to shown that geometric phases exist also for discrete-time driftless nonlinear control systems, but that unlike their continuous-time counterpart, they need not obey any area rule, i.e., even zero-area cycles in shape space can lead to nontrivial geometric phases. When the discrete-time system is obtained through Euler discretization of a continuous-time system, it is shown that the zero-area geometric phase corresponds to the gap between the Euler discretization and an exact discretization of the continuous-time system.

Keywords:Algebraic/geometric methods, Observers for nonlinear systems, Estimation Abstract: A discrete-time attitude state estimation scheme that uses a global representation of the configuration space for rigid body attitude motion, is presented. This estimation scheme uses discrete-time state measurements of inertially known vectors along with rate gyro measurements of the angular velocity, to obtain state estimates in the filtering stage. Additionally, a set of sigma points is obtained from the unscented transform based on exponential coordinates, with re-sampling centered at the current state estimate at each measurement instant. The state estimates along with sampled sigma points are propagated between measurement instants, using a discrete-time attitude state observer that is almost globally finite-time stable. The propagated sigma points and state estimate are enclosed by a minimum volume ellipsoid at the measurement instant. It is assumed that all states are measured at a constant measurement sample rate and that state measurement errors, expressed in the exponential coordinates, are bounded by an ellipsoidal bound. The update stage of the filter consists of finding the minimum trace ellipsoid that contains the intersection of this measurement uncertainty bound and the minimum volume ellipsoid enclosing the propagated sigma points. This updated ellipsoid provides the filtered uncertainty bound and its center provides the updated state estimate. A new set of sigma points is selected from this ellipsoid and the propagation and update steps are repeated between measurement instants. Numerical simulation results confirm the analytically obtained stability properties of the attitude state observer. Numerical results also show that state estimate errors are bounded in the presence of bounded measurement noise and bounded disturbance torque.

A new geometric approach based on unification of D-stability approach, canonical parameter space approach and D-decomposition approach to the unconstrained parametric stability problem is presented.

Topology and adjacencies the sets of monic complex polynomials with fixed distributions of roots relative to an arbitrary semialgebraic stability region Omega are described.

These results are obtained through the application of topological theory of symmetric products based on analysis of correspondence between roots and coefficients of an indeterminate polynomial.

Keywords:Algebraic/geometric methods, Switched systems, Linear systems Abstract: This paper considers the disturbance decoupling problem for switched discrete-time linear systems, where switching occurs within a set of admissible transitions defined via a weighted directed graph. The concept of subspace arrangement, as a collection of linear subspaces, is employed as a main tool for the definition of geometric properties tailored to switched linear systems on digraphs. Appropriate forms of feedback laws that achieve disturbance decoupling under certain classes of admissible switching signals are characterized in terms of strong and weak notions of controlled invariance. The result extends previous approaches based on robust controlled invariance, to the special class of switched discrete-time linear systems over digraphs based on stratified controlled invariance.

Keywords:Output regulation, Hybrid systems Abstract: In this paper, the robust output regulation problem for linear hybrid systems in the presence of periodic jumps is considered. The solution is provided in terms of an External Model, as opposed to the classical implementation of an Internal Model, providing a suitable steady-state signal to the pre-stabilized plant. The construction of the External Model does not rely on the exact knowledge of any value defining the plant or its interconnection with the exosystem and it is based merely on input-output data. The design consists essentially in two different phases: firstly, the steady-state relation between the output error and the state of the External Model unit is estimated by means of input-output measurements, and, second, such estimate is exploited to suitably update the state of the External Model in order to generate the correct steady-state signal achieving regulation, in such a way that the original asymptotic stability property of the plant is not affected by the reset mechanism.

Keywords:Predictive control for nonlinear systems, Output regulation, Computational methods Abstract: In many applications, it is necessary to design controllers that enable the system output to track a time-varying reference signal. In this paper, a low-complexity sampling-based output tracking explicit nonlinear model predictive controller (ENMPC) is proposed for a class of bounded, time-varying reference signals, where only the bounds on the family of admissible reference signals are known to the designer a priori. The basic idea is to sample the state and reference space using deterministic sampling and construct the ENMPC by using linear regression. Feasibility and stability guarantees are provided and the effectiveness of the proposed approach is demonstrated via a numerical example.

Keywords:Output regulation, Robust adaptive control, Direct adaptive control Abstract: This paper presents the current developments of a novel approach to robust Adaptive Feedforward Control (AFC) of uncertain linear systems affected by harmonic disturbance of known frequency. The features that set the proposed method apart from existing ones are the following: (i) knowledge of the sign of both the real and imaginary parts of the transfer function at the frequency of excitation is not needed; (ii) persistence of excitation is not required; (iii) stability analysis tools based on averaging are avoided, hence the requirement of an exponentially stable equilibrium is circumvented. The methodology reposes upon recent results on adaptive regulation of uncertain linear systems with weak immersions as well as on classic tools in adaptive control. A noticeable drawback of the proposed controller - at this stage of the research - is its relatively high dimensionality, which stems from the necessity of a convexification of a non-convex parameter set.

Keywords:Output regulation, Stability of nonlinear systems, Mechanical systems/robotics Abstract: This paper addresses the output regulation problem of rigid bodies whose kinematic configuration space lies on the Special Euclidean Group SE(3). Reference trajectories to be tracked are generated by an autonomous system, referred to as exosystem, defined on the Special Euclidean Group as well. Only partial relative pose measurements associated to the ``natural" linear left group action on SE(3) along with the pose and the velocity of the controlled body are available. The proposed control action embeds a copy of the exosystem kinematics properly updated by means of relative information error in the same spirit of internal model principle.

Keywords:Output regulation Abstract: In this paper we introduce the low-power high-gain observer, developed in [1], to solve problems of output regulation for nonlinear systems. We show how the new tool makes it possible the implementation of high dimensional controllers, that tipically arise when the ideal steady-state control that must be generated to secure zero regulation error is affected by uncertainties.

Keywords:Agents-based systems, Output regulation, Cooperative control Abstract: In this paper, we consider the cooperative output regulation problem for heterogeneous linear multi-agent systems in the presence of communication constraints. Under standard assumptions on the agents dynamics, we propose a distributed control algorithm relying on intermittent and asynchronous discrete-time information exchange that can be subject to unknown time-varying delays and information losses. We show that cooperative output regulation can be reached for arbitrary characteristics of the discrete-time communication process and under mild assumptions on the interconnection topology between agents. A numerical example is given to illustrate the effectiveness of our theoretical results.

Keywords:Supervisory control, Automata, Discrete event systems Abstract: We study supervisor localization for timed discrete-event systems under partial observation in the Brandin-Wonham framework. First, we employ timed relative observability to synthesize a partial-observation monolithic supervisor; the control actions of this supervisor include not only disabling action of prohibitible events (as that of controllable events in the untimed case) but also "clock-preempting" action of forcible events. Accordingly we decompose the supervisor into a set of partial-observation local controllers one for each prohibitible event, as well as a set of partial-observation local preemptors one for each forcible event. We prove that these local controllers and preemptors collectively achieve the same controlled behavior as the partial-observation monolithic supervisor does. In the resulting local controllers/preemptors, only observable events can cause state change. The results are illustrated by a timed workcell example.

Keywords:Supervisory control, Cooperative control Abstract: Sequential composition is a supervisory control architecture for addressing control problems in complex dynamical systems. Although sequential composition works properly for a single system, it is not designed for cooperative systems. This paper extends the standard sequential composition by introducing a novel approach to compose multiple sequential composition controllers towards cooperative control. Given two or more systems, cooperation is achieved by composing each of the systems' control automaton, together with estimation for the domains of attraction of the resulting composed controllers. This typically results in new events for the original sequential composition controllers. Applying these events, the cooperative control system can fulfill the tasks which are not possible to satisfy with the original controllers individually. The simulation results of an inverted pendulum system collaborating with two second-order DC motors are presented for cooperative swing-up maneuvers.

Keywords:Supervisory control, Discrete event systems, Agents-based systems Abstract: This paper presents a Directed Controller Synthesis (DCS) technique for discrete event systems. This DCS method explores the solution space for reactive controllers guided by a domain-independent heuristic. The heuristic is derived from an efficient abstraction of the environment based on the componentized way in which complex environments are described. Then by building the composition of the components on-the-fly DCS obtains a solution by exploring a reduced portion of the state space. This work focuses on untimed discrete event systems with safety and co-safety (i.e. reachability) goals. An evaluation for the technique is presented comparing it to other well-known approaches to controller synthesis (based on symbolic representation and compositional analyses).

Keywords:Supervisory control, Discrete event systems, Hierarchical control Abstract: In this work we employ hierarchy in order to greatly reduce the computational complexity for generating the optimal control for a discrete event system. Specifically, we propose a formal notion of equivalence we term cost equivalence that we use to generate an abstraction of a weighted automaton representing a supervisory controller. We demonstrate that this abstraction can be employed for planning, even in the presence of events that cannot be controlled. Furthermore, we propose additional requirements that we show guarantee that the plan generated from the abstracted automaton achieves optimal behavior when applied to the original unabstracted automaton. The results we generate in this paper have application to a broad class of graph-search problems.