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Recently, Thompson sampling has been shown to achieve good theoretical performance guarantees for stochastic control problems with parameter uncertainty when the state, control, and parameter spaces are all finite. Much less is known however about the performance of Thompson sampling when applied to continuous or more general spaces, which constitutes an important class of problems in practice. In this paper, we study Thompson sampling when applied to a broad class of average cost stochastic control problems where the state, control, and parameter spaces are all general measurable spaces. The main contributions of our paper are establishing theoretical performance guarantees for Thompson sampling as measured by: first, expected posterior sampling error; and second, average per period regret. [ABSTRACT FROM AUTHOR]

In this paper, we address the so-called Liouville control problem for discrete-time SISO linear systems in the class of Gaussian distributions. In particular, we propose a systematic procedure for the characterization of a dynamic output feedback policy that will transfer the output of the system, which is a known Gaussian random variable, to a goal Gaussian distribution after a finite number of stages. In the proposed approach, the Liouville control problem is reduced to two decoupled (finite-dimensional) quadratic programs, one of which is subject to a single affine constraint, which is a convex program, whereas the other one is subject to a single quadratic equality constraint. Despite the fact that the second optimization problem is not convex, one can characterize its exact solution via a systematic procedure without resorting to convex relaxation techniques, which may yield suboptimal or even infeasible solutions to the original (nonconvex) optimization problem. Finally, we present numerical simulations that illustrate the key ideas of this paper. [ABSTRACT FROM AUTHOR]

This paper studies the consensus tracking problem of uncertain Lagrangian systems. In contrast to the existing results where the command signals are sufficiently smooth, we consider a class of nonsmooth command signals generated by a switched command generator, which might be more realistic from the perspective of practical applications. The main technical innovations of this paper are threefold. First, to enable a rigorous problem formulation, some piecewise decaying function sets are defined to precisely describe the steady-state behaviors of the tracking errors. Second, to ensure the stability of the switched nonlinear closed-loop system, a system-based scaling method with the establishment of several lemmas is developed to determine the minimal dwell time of the switching signal. Third, a quantitative analysis is performed to acquire the ultimate bound for the steady-state tracking errors. The proposed control approach is evaluated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min–max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush–Kuhn–Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption. [ABSTRACT FROM AUTHOR]

This paper studies the optimal decentralized state-feedback control of large-scale systems. The large-scale system is composed of subsystems and defined over a connected digraph. One step time is required for information to travel across an edge in the graph. Under the above-mentioned setup, when subsystem process noises are uncorrelated, the explicit optimal state-feedback controller can be designed by independence decomposition based on information hierarchy graph. However, this decomposition method fails when the subsystem process noises are correlated. In this paper, we propose a new decomposition method for system state and control input, and split the optimal state-feedback control problem with correlated process noises into two subproblems that can be solved separately. The solution to the first subproblem can be obtained by solving a linear matrix equation. The second subproblem is solved by algebraic Ricatti equation. [ABSTRACT FROM AUTHOR]

The issue of cyber-security has become ever more prevalent in the analysis and design of networked systems. In this paper, we analyze networked control systems in the presence of denial-of-service (DoS) attacks, namely attacks that prevent transmissions over the network. We characterize frequency and duration of the DoS attacks under which input-to-state stability (ISS) of the closed-loop system can be preserved. To achieve ISS, a suitable scheduling of the transmission times is determined. It is shown that the considered framework is flexible enough so as to allow the designer to choose from several implementation options that can be used for trading-off performance versus communication resources. Examples are given to substantiate the analysis. [ABSTRACT FROM AUTHOR]

This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation to an optimization problem, which is solved via a new policy iteration method. The proposed method distinguishes from previously known nonlinear ADP methods in that the neural network approximation is avoided, giving rise to significant computational improvement. Instead of semiglobally or locally stabilizing, the resultant control policy is globally stabilizing for a general class of nonlinear polynomial systems. Furthermore, in the absence of the a priori knowledge of the system dynamics, an online learning method is devised to implement the proposed policy iteration technique by generalizing the current ADP theory. Finally, three numerical examples are provided to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of determining the \cal H\infty and \cal H2 norms of 2-D mixed continuous-discrete-time systems. The first contribution is to propose a novel approach based on the use of complex Lyapunov functions with even rational parametric dependence, which searches for upper bounds on the sought norms via linear matrix inequalities (LMIs). The second contribution is to show that the upper bounds provided are nonconservative by using Lyapunov functions in the chosen class with sufficiently large degree. The third contribution is to provide conditions for establishing the tightness of the upper bounds. The fourth contribution is to show how the numerical complexity of the proposed approach can be significantly reduced by proposing a new necessary and sufficient LMI condition for establishing positive semidefiniteness of even Hermitian matrix polynomials. This result is also exploited to derive an improved necessary and sufficient LMI condition for establishing exponential stability of 2-D mixed continuous-discrete-time systems. Some numerical examples illustrate the proposed approach. It is worth remarking that nonconservative LMI methods for determining the \cal H\infty and \cal H2 norms of 2-D mixed continuous-discrete-time systems have not been proposed yet in the literature. [ABSTRACT FROM PUBLISHER]

This paper studies the convergence time of dual gradient methods for general (possibly nondifferentiable) strongly convex programs. For general convex programs, the convergence time of dual subgradient/gradient methods with simple running averages (running averages started from iteration 0) is known to be O(\frac1\epsilon ^2). This paper shows that the convergence time for general strongly convex programs is O(\frac1\epsilon ) . This paper also considers a variation of the average scheme, called the sliding running averages, and shows that if the dual function of the strongly convex program is locally quadratic then the convergence time of the dual gradient method with sliding running averages is O(\log (\frac1\epsilon )). The convergence time analysis is further verified by numerical experiments. [ABSTRACT FROM PUBLISHER]

In this paper, we apply Thompson sampling to a class of average reward stochastic control problems with parameter uncertainty. Specifically, we study an average reward stochastic control problem over an infinite horizon in which both the reward and state transition distributions are parameterized by an unknown parameter taking values in a finite space. The main result of this paper is a proof showing that Thompson sampling achieves a worst case average per period regret of O(T^-1), which is asymptotically optimal. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the stability (gain and phase) margin of networked dynamical systems, e.g., vehicles in formation, each of which has access to the state of its neighbors and subsequently uses a state feedback gain $F$ for a certain global objective such as attitude synchronization. Here, the network topology is directed and described by a generalized Laplacian matrix $L$. An individual dynamical system can adopt its own state feedback control law such as a linear-quadratic-regulator controller for an ample stability margin, but it may lose the stability margin to a great extent when the same control strategy utilizing relative state information is used after being interconnected with other dynamical systems. This paper reveals and elaborates upon the following four facts: First, the stability margin after interconnection is quantified via the minimum singular value of a frequency-dependent matrix made up of $F$ and $L$; Second, the stability margin of a networked dynamical system having a pole at the origin is at most the inverse of the zero-eigenvalue sensitivity of $L$; Third, there exists an upper bound of the stability margin that has a computational merit, and asymptotically converges to the exact margin with respect to network size, probability of link existence, and control gain in a random network setting; and finally, $L$ can be designed to maximize the stability margin. Numerical examples are provided to demonstrate the elaboration. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including predictive control scheme, stochastic feedback control and monotone systems.

Provides an overview of the technical articles and features presented in this issue. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of establishing stability of nonlinear interconnected systems. This paper introduces a mathematical formulation of the state-dependent scaling problems whose solutions directly provide Lyapunov functions proving stability properties of interconnected dissipative systems in a unified manner. Stability criteria are interpreted as sufficient conditions for the existence of solutions to the state-dependent scaling problems. Computing solutions to the problems is straightforward for systems covered by classical stability criteria. It, however, could be too difficult for systems with strong nonlinearity. The main purpose of this paper is to demonstrate the effectiveness beyond formal applicability by focusing on interconnected integral input-to-state stable (iISS) systems and input-to-state stable (ISS) systems. This paper derives small-gain-type theorems for interconnected systems involving iISS systems from the state-dependent scaling formulation. This paper provides solutions and Lyapunov functions explicitly. The new framework seamlessly generalizes the ISS small-gain theorem and classical stability criteria such as the Lp small-gain theorem, the passivity theorems, the circle, and Popov criteria. State-dependence of the scaling is crucial for effective treatment of essential nonlinearities, while constants are sufficient for classical nonlinearities. [ABSTRACT FROM AUTHOR]

This paper studies the linear-time temporal logic (LTL) control of a class of fair discrete-event systems (DESs). It is motivated by the curious extent in which the use of LTL can be strengthened and differentiated in control theory development. Over a fair DES model, a marker-progressive supervisory control problem is formulated in LTL. The problem formulation admits a more flexible specification of multiple markers to distinguish different DES tasks, and seeks to find a supervisor—a passive control function by convention for specified temporal safety—such that a fair DES under its control is guaranteed to make constant progress to these markers. The problem is studied in terms of DES marker-controllability—a new controllability concept formulation of temporal safety for constant marker progress. This new formulation sheds light on how event fairness in DESs coachieves such marker progress with supervision that exists. It is shown that a solution supervisor may be found by canonical LTL verification. Three examples are provided for illustration. [ABSTRACT FROM AUTHOR]

This paper considers one of the fundamental issues in design and analysis of sampled multidimensional systems—that of uncertainty modeling and robust stability analysis. Methods of structured uncertainty analysis (µ-analysis) are extended toward systems with dynamical and noncausal spatial coordinates. The stability is understood in a broad sense and includes decay (localization) of system response along the noncausal spatial coordinates. Robustness of dynamical stability and spatial localization of response and boundary effects are addressed in a unified way. The main technical condition enabling the technical results of the paper is that the feedback loop including a multidimensional plant and controller does not have a feed-through in the dynamical (time) coordinate sense. As an example, this paper applies the multidimensional structured uncertainly analysis to closed-loop control of a cross-directional paper machine process. The paper formulates multidimensional models of the process, its controller, and a structured uncertainty. The uncertainty corresponds to a combination of errors in the actuator mapping, the cross-directional response gain, and the response width. [ABSTRACT FROM AUTHOR]

This paper addresses a supervisory control problem for time invariant hybrid dynamical systems based on the $l$-complete approximation scheme by Moor and Raisch (“Discrete supervisory control of hybrid systems based on $l$-complete approximations,” 2002) and partial observation. An underlying hybrid plant is realized by a hybrid state machine with an infinite state space, and its external behavior is described by discrete input/output signals with finite range, and some output signal is assumed to be unmeasurable. For the strongest $l$-complete approximation of the plant, which is realized by a finite state machine, we present a method to design a finite state supervisor to achieve a given specification. The supervisor cannot observe the unmeasurable output signal. Finally, we show that the finite state supervisor also meets the specification for the underlying hybrid plant. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of synchronization in networks of heterogeneous agents with common nominal behavior. The agents are modeled as (possibly nonlinear) perturbed versions of a common SISO nominal LTI operator, and they are interconnected via a sparse memoryless interconnection operator, coherent with the communication graph underlying the network. The network is said to synchronize if the outputs of the agents tend to align along given directions, the most important case being consensus, or agreement. The paper provides a general result, based on IQCs, that ensures synchronization of the network with robustness w.r.t. uncertainties in the interconnection and in each agent's dynamics. Scalability issues are discussed in the scenario where the interconnection operator is a constant normal matrix, yielding the generalization of the very popular linear consensus algorithm. The wide range of applicability of the proposed criterion is shown by providing synchronization conditions in some important examples. Whenever possible, graphical criteria are proposed for checking the required conditions. [ABSTRACT FROM PUBLISHER]

In this paper, we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting, where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function, and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Checking validity of a model is a crucial step in the process of system identification. This is especially true when dealing with switched affine systems since, in this case, the problem of system identification from noisy data is known to be generically NP-Hard and can only be solved in practice by using heuristics and relaxations. Therefore, before the identified models can be used for instance for controller design, they should be systematically validated against additional experimental data. In this paper we address the problem of model (in)validation for multi-input multi-output switched affine systems in output error form with unknown switches. As a first step, we prove that necessary and sufficient invalidation certificates can be obtained by solving a sequence of convex optimization problems. In principle, these problems involve increasingly large matrices. However, as we show in the paper by exploiting recent results from semialgebraic geometry, the proposed algorithm is guaranteed to stop after a finite number of steps that can be be explicitly computed from the a priori information. In addition, this algorithm exploits the sparse structure of the underlying optimization problem to substantially reduce the computational burden. The effectiveness of the proposed method is illustrated using both academic examples and a non-trivial problem arising in computer vision: activity monitoring. [ABSTRACT FROM AUTHOR]

This paper considers the state estimation problem for the general continuous-time Stochastic Hybrid System (SHS) which has various applications. Defined on the hybrid state space, the SHS has the interacting discrete dynamics and continuous dynamics subject to various uncertainties. The hybrid state estimation problem is to estimate both the continuous state and the discrete state of the SHS with the information given by a continuous-time observation process. In this paper, the hybrid state estimation problem is mathematically formulated and the corresponding filtering equations that are stochastic partial differential equations are derived to describe the evolution of the hybrid state estimates conditioned on the observation history. A numerical algorithm based on a finite-difference approach is proposed to solve the filtering equations. A Markov Chain (MC) is constructed on the descretized hybrid state space to approximate the infinitesimal generator of the SHS and then hybrid state estimation for the SHS is reduced to estimating the state of the MC. It is proved that the state estimation results of the MC converge to the solution to the filtering equations as the constructed MC converges to the SHS. An illustrative example of aircraft tracking is used to demonstrate the performance of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the output synchronization problem for a network of heterogeneous diffusively-coupled nonlinear agents. Specifically, we show how the (heterogeneous) agents can be controlled in such a way that their outputs asymptotically track the output of a prescribed nonlinear exosystem. The problem is solved in two steps. In the first step, the problem of achieving consensus among (identical) nonlinear reference generators is addressed. In this respect, it is shown how the techniques recently developed to solve the consensus problem among linear agents can be extended to agents modeled by nonlinear $d$-dimensional differential equations, under the assumption that the communication graph is connected. In the second step, the theory of nonlinear output regulation is applied in a decentralized control mode, to force the output of each agent of the network to robustly track the (synchronized) output of a local reference model. Simulation results are presented to show the effectiveness of the design methodology. [ABSTRACT FROM PUBLISHER]

Consensus of a network with a directed acyclic graph, a directed graph with no directed cycles, is always guaranteed if it contains a spanning tree. This paper studies the effect of adding edges to a directed acyclic graph that may result in a directed cycle. It is shown that the effect on consensus performance of the whole network is only determined by a local subnetwork containing all the added edges. More specifically, both a one-dimensional (1-D) chain network and a 2-D grid network are investigated in this paper. It is proved that, when a reverse edge is added, the consensus performance is degraded by the amount only determined by the edge range, that is, independent of the network size or the location of the added edge. [ABSTRACT FROM AUTHOR]

In this paper, a unified framework is established to investigate both the quantized and the saturated control problems for a class of sampled-data systems under noisy sampling intervals. A random variable obeying the Erlang distribution is used to describe the noisy sampling intervals. In virtue of the matrix exponential, the sampled-data control system is transformed into an equivalent discrete-time stochastic system, and the aim of this paper is to design a quantized/saturated sampled-data controller such that the resulting discrete-time stochastic system is stochastically stable when the sampling error follows the Erlang distribution. In order to deal with the case of multiple control inputs, a confluent Vandermonde matrix approach is proposed in the design process. By using the Kronecker product operation and the matrix inequality techniques, the desired quantized/saturated controller gains are designed in terms of the solution to certain matrix inequalities. Finally, a simulation example is exploited to verify the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

This paper addresses the stabilization problem for nonlinear Markovian jump systems (MJS) with output disturbances, actuator and sensor faults simultaneously. This kind of plants are common in practical systems, such as mobile manipulators with switching joints. In this paper, a sliding mode observer design scheme is proposed for a new descriptor augmented plant. By employing the developed observer, the effects of actuator and sensor faults can be eliminated. It is shown that the stabilization of the overall closed-loop plant can be guaranteed by the proposed fault tolerant control (FTC) scheme. Finally, an example concerning mobile manipulators with Markovian switching joints is presented to show the effectiveness and applicability of the theoretical results. [ABSTRACT FROM AUTHOR]

Provides an overview of the technical articles and features presented in this issue. [ABSTRACT FROM AUTHOR]

This paper is concerned with the energy shaping of 1-D linear boundary controlled port-Hamiltonian systems. The energy-Casimir method is first proposed to deal with power preserving systems. It is shown how to use finite dimensional dynamic boundary controllers and closed-loop structural invariants to partially shape the closed-loop energy function and how such controller finally reduces to a state feedback. When dissipative port-Hamiltonian systems are considered, the Casimir functions do not exist anymore (dissipation obstacle) and the immersion (via a dynamic controller)/reduction (through invariants) method cannot be applied. The main contribution of this paper is to show how to use the same ideas and state functions to shape the closed-loop energy function of dissipative systems through direct state feedback i.e. without relying on a dynamic controller and a reduction step. In both cases, the existence of solution and the asymptotic stability (by additional damping injection) of the closed-loop system are proven. The general theory and achievable closed-loop performances are illustrated with the help of a concluding example, the boundary stabilization of a longitudinal beam vibrations. [ABSTRACT FROM AUTHOR]

We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. For those systems, the Lie logarithm of the error turns out to obey a linear differential equation. Then, we leverage this “log-linear” property of the error evolution, to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of marking estimation in labeled Petri nets whose initial marking is known to belong to a given convex set, in the presence of silent transitions (i.e., transitions labeled with the empty word) and indistinguishable transitions (i.e., transitions sharing the same label with other transitions). First, we demonstrate that all sets of markings consistent with a given sequence of observations can be described in linear algebraic terms (as a union of convex sets); subsequently, this observation is used to construct (offline) a marking observer under appropriate boundedness assumptions. Using the marking observer we show how to derive, at design time, a state feedback control law under the assumption that all transitions sharing a label can be enabled or disabled simultaneously as a group; this way, the most burdensome part of the computations is performed offline. [ABSTRACT FROM AUTHOR]

The article presents abstracts of several articles including "On Repetitive Scenario Design," by G. C. Calafiore, "Accessibility of Nonlinear Time-Delay Systems," C. Califano and C. H. Moog and "Anytime Capacity of a Class of Markov Channels," by P. Minero and M. Franceschetti.

In this two-part paper we study stabilization and optimal control of linear time-invariant systems with stochastic multiplicative uncertainties. We consider structured multiplicative perturbations, which, unlike in robust control theory, consist of static, zero-mean stochastic processes, and we assess the stability and performance of such systems using mean-square measures. While Part 2 of this paper tackles and solves optimal control problems under the mean-square criterion, Part 1 is devoted to the stabilizability problem. We develop fundamental conditions of mean-square stabilizability which ensure that an open-loop unstable system can be stabilized by output feedback in the mean-square sense. For single-input single-output systems, a general, explicit stabilizability condition is obtained. This condition, both necessary and sufficient, provides a fundamental limit imposed by the system's unstable poles, nonminimum phase zeros and time delay. For multi-input multi-output systems, we provide a complete, computationally efficient solution for minimum phase systems possibly containing time delays, in the form of a generalized eigenvalue problem readily solvable by means of linear matrix inequality optimization. Limiting cases and nonminimum phase plants are analyzed in depth for conceptual insights, revealing, among other things, how the directions of unstable poles and nonminimum phase zeros may affect mean-square stabilizability in MIMO systems. Other than their independent interest, stochastic multiplicative uncertainties have found utilities in modeling networked control systems pertaining to, e.g., packet drops, network delays, and fading. Our results herein lend solutions applicable to networked control problems addressing these issues. [ABSTRACT FROM AUTHOR]

The aim of this paper is to approximate a Finite-State Markov (FSM) process by another process defined on a lower dimensional state space, called the approximating process, with respect to a total variation distance fidelity criterion. The approximation problem is formulated as an optimization problem using two different approaches. The first approach is based on approximating the transition probability matrix of the FSM process by a lower-dimensional transition probability matrix, resulting in an approximating process which is a Finite-State Hidden Markov (FSHM) process. The second approach is based on approximating the invariant probability vector of the original FSM process by another invariant probability vector defined on a lower-dimensional state space. Going a step further, a method is proposed based on optimizing a Kullback-Leibler divergence to approximate the FSHM processes by FSM processes. The solutions of these optimization problems are described by optimal partition functions which aggregate the states of the FSM process via a corresponding water-filling solution, resulting in lower-dimensional approximating processes which are FSHM or FSM processes. Throughout the paper, the theoretical results are justified by illustrative examples that demonstrate our proposed methodology. [ABSTRACT FROM AUTHOR]

This paper concerns state estimation problems in a mean field control setting. In a finite population model, the goal is to estimate the joint distribution of the population state and the state of a typical individual. The observation equations are a noisy measurement of the population. The general results are applied to demand dispatch for regulation of the power grid, based on randomized local control algorithms. In prior work by the authors it is shown that local control can be designed so that the aggregate of loads behaves as a controllable resource, with accuracy matching or exceeding traditional sources of frequency regulation. The operational cost is nearly zero in many cases. The information exchange between grid and load is minimal, but it is assumed in the overall control architecture that the aggregate power consumption of loads is available to the grid operator. It is shown that the Kalman filter can be constructed to reduce these communication requirements, and to provide the grid operator with accurate estimates of the mean and variance of quality of service (QoS) for an individual load. [ABSTRACT FROM AUTHOR]

Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show global linear convergence rate bounds for Douglas-Rachford splitting and ADMM under strong convexity and smoothness assumptions. We further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters. For problems that satisfy the assumptions, we show how to select step-size and metric for the algorithm that optimize the derived convergence rate bounds. For problems with a similar structure that do not satisfy the assumptions, we present heuristic step-size and metric selection methods. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the optimal distributed control (ODC) problem for linear discrete-time deterministic and stochastic systems. The objective is to design a static distributed controller with a prespecified structure that is globally optimal with respect to a quadratic cost functional. It is shown that this NP-hard problem has a quadratic formulation, which can be relaxed to a semidefinite program (SDP). If the SDP relaxation has a rank-1 solution, a globally optimal distributed controller can be recovered from this solution. By utilizing the notion of treewidth, it is proved that the nonlinearity of the ODC problem appears in such a sparse way that an SDP relaxation of this problem has a matrix solution with rank at most 3. Since the proposed SDP relaxation is computationally expensive for a large-scale system, a computationally cheap SDP relaxation is also developed with the property that its objective function indirectly penalizes the rank of the SDP solution. Various techniques are proposed to approximate a low-rank SDP solution with a rank-1 matrix, leading to near globally optimal controllers together with a bound on the optimality degree of each controller. The above results are developed for both finite-horizon and infinite-horizon ODC problems. The SDP relaxations developed in this work are exact for the design of a centralized controller, hence serving as an alternative for solving Riccati equations. The efficacy of the proposed SDP relaxations is elucidated through a case study on the distributed frequency control of power systems. [ABSTRACT FROM PUBLISHER]

In this paper, we present a hierarchical, iterative distributed optimization algorithm and show that the algorithm converges to the global solution of a particular optimization problem. The motivation for the distributed optimization problem is the predictive control of a smart grid, in which the states of charge of a network of residential-scale batteries are optimally coordinated so as to minimize variability in the aggregated power supplied to/from the grid by the residential network. The distributed algorithm developed in this paper calls for communication between a central entity and an optimizing agent associated with each battery, but does not require communication between agents. The distributed algorithm is shown to achieve the performance of a large-scale centralized optimization algorithm, but with greatly reduced communication overhead and computational burden. A numerical case study using data from an Australian electricity distribution network is presented to demonstrate the performance of the distributed optimization algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we establish results similar in nature to the invariance principle for a class of stochastic hybrid systems modeled by set-valued mappings. In particular, we characterize the set to which bounded random solutions converge in terms of a new concept called weak total recurrence. A refinement of the result under the existence of a non-increasing on average Lyapunov-like function is also established. A comparison between weak total recurrence and the frequently studied invariance concepts are presented. Finally, application of the main results to establish weak sufficient conditions for certifying stochastic stability properties like uniform global asymptotic stability in probability for compact sets and uniform global recurrence for open, bounded sets are discussed. [ABSTRACT FROM PUBLISHER]

This paper proposes an approach to control of discrete systems with incomplete information and sensing capabilities, with respect to temporal logic constraints. The approach introduces active sensing to alleviate computational effort in control design for systems interacting with uncontrollable environments under incomplete information. Particularly, it transforms a deterministic controller under complete information into a randomized, observation-based controller. Interleaving the latter with strategic queries to sensors, the temporal logic specification is proven to be satisfied almost surely. The effectiveness of the method is demonstrated with robotic motion planning examples. [ABSTRACT FROM PUBLISHER]

These instructions give guidelines for preparing papers for this publication. Presents information for authors publishing in this journal. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses articles in the issue on topics including model-based fault detection and isolation approach for the monitoring of nonlinear large-scale systems; integration of relative localization; and control problem for linear discrete-time systems.

The author discusses about his longevity as editor-and-chief of "IEEE Transactions on Automatic Control." He notes that he lasted as editor-in-chief because the position give him opportunities to learn continually and he tried to appreciate its lighter side. He recounts the major highlights in the operation of the journal including the introduction of a web-based system for submitting and reviewing papers. He also expressed his gratitude to his colleagues including John Baillieul.

An introduction is presented which discusses several articles within the issue on topics including time-nonhomogeneous continuous Markov processes; distributed algorithm for nonconvex optimization problems; and convergence rates for consensus-based stochastic gradient descent algorithms.