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In this paper, we study the cooperative output consensus problem of discrete-time heterogeneous multi-agent systems over nonidentical channel fading networks. Different from the traditional output consensus problem, the communication channels among agents are perturbed by stochastic multiplicative noises, which can also describe the packet loss phenomenon. The perturbed channels can result in a significant challenge for consensus analysis since their effect cannot be separated linearly from the communication topology. Based on the distributed feedforward control method, a novel distributed dynamic output feedback controller is developed to ensure output synchronization for each agent in the mean-square sense. To facilitate the consensus analysis, we utilize the relationship between the graph Laplacian matrix and the incidence matrix and matrix transformation technique, and find sufficient solvability conditions relying on each agent's dynamics, the maximum eigenvalue of communication graph and the packet loss probability for the scenarios of undirected graph and directed graph, respectively. Finally, simulation results are given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of general linear forward and , backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient conditions for the existence of a (unique) solution to FBSDEs are given in terms of a Riccati equation. Two kinds of stochastic LQ optimal control problem are then studied as applications. First, we derive the optimal solution to the classic stochastic LQ problem by applying the solution to the associated FBSDEs. Secondly, we study a new type of LQ problem governed by a forward–backward stochastic system (FBSS). By applying the maximum principle and the solution to FBSDEs, an explicit solution is given in terms of a Riccati equation. Finally, by exploring the asymptotic behavior of the Riccati equation, we derive an equivalent condition for the mean-square stabilizability of FBSS. [ABSTRACT FROM AUTHOR]

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of non-standard forward–backward stochastic differential equations (FBSDEs). By solving the FBSDEs, we design a set of decentralized strategies by virtue of two differential Riccati equations. Instead of the ɛ -Nash equilibrium in classical mean-field games, the set of decentralized strategies is shown to be a Nash equilibrium. For the infinite-horizon problem, a simple condition is given for the solvability of the algebraic Riccati equation arising from consensus. Furthermore, the social optimal control problem is studied. Under a mild condition, the decentralized social optimal control and the corresponding social cost are given. [ABSTRACT FROM AUTHOR]

This paper is concerned with mean field linear quadratic social control with common noise, where the weight matrices of individual costs are indefinite We first obtain a set of forward–backward stochastic differential equations (FBSDEs) from variational analysis, and then construct a centralized feedback representation by decoupling the FBSDEs. By using solutions of two Riccati equations, we design a set of decentralized control laws, which is further shown to be asymptotically social optimal. The necessary and sufficient conditions are given for uniform stabilization of the systems by exploiting the relation between population state average and aggregate effect. An explicit expression of the optimal social cost is given in terms of two Riccati equations. Besides, the decentralized optimal solution is provided for mean field social control problem with finite agents. [ABSTRACT FROM AUTHOR]

This study deals with the problem of consensus error calculation for linear multi-agent systems (MASs) with system noises and measurement noises. It is supposed that there exist communication noises when the information exchanges among distinct agents. The agents cannot reach consensus due to the existence of the system noises. We aim to design proper distributed control protocol to calculate the consensus error for the MASs. The states of each agent and its neighbors are estimated by applying Kalman-filtering theory. The distributed control protocol is designed by employing the estimated state information. Then the consensus error is calculated via the unique solution of a Lyapunov equation. Finally, a simulation example is presented to verify the correctness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper considers the recovery of sparse initial state for deterministic discrete-time linear time-invariant systems based on the compressed sensing theory. A class of deterministic linear systems with the global observation matrices satisfying the restricted isometry property (RIP) is characterized. Sufficient conditions on the measurement time instants that guarantee the global observation matrix to be a RIP matrix are obtained. With respect to the recovery of the sparse initial state of a high-dimensional linear system, it is worth mentioning that the number of measurements can be significantly decreased in terms of compressed sensing theory. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the linear quadratic (LQ) control problem for the Itô-type stochastic system with input delays. Due to simultaneous appearances of diffusion terms (dependent on the state and the control) as well as delays in the dynamic system, the problem is very involved and remains to be solved. We not only provide the solvable condition of the problem but also the explicit expression of the causal and adapted controller for a kind of LQ problems. All of these are based on a stochastic Riccati equation. The key technique is to pursue the explicit cost value of the LQ problem by FBSDE and derive the analytical controller via the interplay between the original problem and its equivalent abstract description. [Copyright &y& Elsevier]

Abstract: This paper is concerned with optimal filter problems for networked systems with random transmission delays, while the delay process is modeled as a multi-state Markov chain. By defining a delay-free observation sequence, the optimal filter problems are transformed into ones of the Markov jumping parameter system. We first present an optimal Kalman filter, which is with time-varying, path-dependent filter gains, and the number of the paths grows exponentially in time delay. Thus an alternative optimal Markov jump linear filter is presented, in which the filter gains just depend on the present value of the Markov chain. Further, an optimal filter with constant-gains is developed, the existence condition for the stabilizing solutions to the filter is given, and it can be shown that the proposed Markov jump linear filter converges to the constant-gain filter under appropriate assumptions. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the consensus of multi-agent systems with input delay. Among all standard static protocols that achieve the consensus for the multi-agent system under no input delay, we aim to find the maximum input delay such that the system remains consensusable under the same protocols. In the case of continuous-time systems, in view of the continuity of stability with respect to the time delay, the maximum delay margin for consensusability is given for scalar systems and vector systems with a single unstable open-loop pole. For scalar discrete-time systems, we show that the maximum delay margin for consensusability is strictly greater than zero if and only if the open-loop pole of the system is located in a specified interval. [Copyright &y& Elsevier]

Abstract: This paper considers the stochastic LQR problem for systems with input delay and stochastic parameter uncertainties in the state and input matrices. The problem is known to be difficult due to the presence of interactions among the delayed input channels and the stochastic parameter uncertainties in the channels. The key to our approach is to convert the LQR control problem into an optimization one in a Hilbert space for an associated backward stochastic model and then obtain the optimal solution to the stochastic LQR problem by exploiting the dynamic programming approach. Our solution is given in terms of two generalized Riccati difference equations (RDEs) of the same dimension as that of the plant. [Copyright &y& Elsevier]

Abstract: This paper studies the shunting cellular neural networks with variable coefficients and time-varying delays. By applying Dini derivative and introducing many real parameters, a series of new and useful criteria on the existence and local exponential stability for general shunting inhibitory cellular neural networks have been derived. Those results obtained in this paper extend and generalize the corresponding results existing in the previous literature. [Copyright &y& Elsevier]

Abstract: In this Letter, power control problem is firstly studied at an angle of LQG measurement-feedback control problem. A stochastic uplink power control problem is considered for CDMA systems. An effective distributed algorithm is proposed based on stochastic linear quadratic optimal control theory assuming SIR measurements contain white noise. The presented scheme minimizes the sum of the power and the error of SIR. A measurement-feedback power controller is designed by constructing an optimization problem of a stochastic linear quadratic type in Krein space and solving the Kalman filter problem for the systems. [Copyright &y& Elsevier]

Abstract: In this paper, the finite horizon mixed control problem is studied for the systems governed by Itô-type nonlinear stochastic differential equations with state, control and external disturbance-dependent noise. It is shown that the mixed control under consideration is associated with the four cross-coupled Hamilton–Jacobi equations. A discrete approximation algorithm is presented for solving the coupled generalized differential Riccati equations arising from linear stochastic control. A necessary condition and a sufficient condition for the existence of the finite horizon stochastic control are derived. In particular, some previous results on deterministic and stochastic control can be viewed as corollaries of our main theorems. [Copyright &y& Elsevier]

Abstract: This paper studies the classic linear quadratic regulation (LQR) problem for both continuous-time and discrete-time systems with multiple input delays. For discrete-time systems, the LQR problem for systems with single input delay has been studied in existing literature, whereas a solution to the multiple input delay case is not known to our knowledge. For continuous-time systems with multiple input delays, the LQR problem has been tackled via an infinite dimensional system theory approach and a frequency/time domain approach. The objective of the present paper is to give an explicit solution to the LQR problem via a simple and intuitive approach. The main contributions of the paper include a fundamental result of duality between the LQR problem for systems with multiple input delays and a smoothing problem for an associated backward stochastic system. The duality allows us to obtain a solution to the LQR problem via standard projection in linear space. The LQR controller is simply constructed by the solution of one backward Riccati difference (for the discrete-time case) or differential (for the continuous-time case) equation of the same order as the plant (ignoring the delays). [Copyright &y& Elsevier]

Abstract: This Letter presents new sufficient conditions of globally exponential stability of neural networks with delays. We show that these results generalize recently published globally exponential stability results. In particular, several different globally exponential stability conditions in the literatures which were proved using different Lyapunov functionals are generalized and unified by using the same Lyapunov functional and the technique of inequality of integral. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks. Those conditions are less restrictive than those given in the earlier references. [Copyright &y& Elsevier]

Abstract: This paper is to study the linear minimum variance estimation for discrete-time systems with instantaneous and -time delayed measurements by using re-organized innovation analysis. A simple approach to the problem is presented in this paper. It is shown that the derived estimator involves solving different standard Kalman filtering with the same dimension as the original system. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the finite horizon fixed-lag smoothing problem for discrete linear time-varying systems. The existence of an smoother is first related to certain inertia condition of an innovation matrix. The innovation matrix is traditionally computed via a Riccati difference equation (RDE) associated with the filtering of an augmented system which is computationally expensive. To avoid solving the RDE of high dimension, we introduce a re-organized innovation and apply innovation analysis and projection theory in Krein space to give a simple method of computing the innovation matrix. The smoother is computed as a projection in Krein space by performing two RDEs of the same dimension as that of the original system. [Copyright &y& Elsevier]

This paper is concerned with a polynomial approach to robust deconvolution filtering of linear discrete-time systems with random modeling uncertainties. The modeling errors appear in the coefficients of the numerators and denominators of both the input signal and system transfer function models in the form of random variables with zero means and known upper bounds of the covariances. The robust filtering problem is to find an estimator that minimizes the maximum mean square estimation error over the random parameter uncertainties and input and measurement noises. The key to our solution is to quantify the effect of the random parameter uncertainties by introducing two fictitious noises for which a simple way is given to calculate their covariances. The optimal robust estimator is then computed by solving one spectral factorization and one polynomial equation as in the standard optimal estimator design using a polynomial approach. An example of signal detection in mobile communication is given to illustrate the effectiveness of our approach. [Copyright &y& Elsevier]

This paper studies the problem of H∞ prediction for linear continuous-time systems. By developing a new method of characterizing the innovation process and applying a novel innovation analysis approach in Krein space, a necessary and sufficient condition for the existence of a finite horizon H∞ predictor is derived. The solution to the H∞ prediction is given in terms of solutions of Riccati and matrix differential equations. We further extend our study to give a necessary and sufficient condition for the H∞ filtering of linear continuous-time systems with both instantaneous and delayed measurements. [Copyright &y& Elsevier]

This paper is concerned with steady-state risk-sensitive filtering, prediction and smoothing problems for discrete-time singular systems. It is shown that a risk-sensitive estimator can be obtained by ensuring the minimum of an indefinite quadratic form to be maximum (minimum) when the risk-sensitivity parameter θ is negative (positive). An auxiliary state-space signal model and an innovation sequence in Krein space are introduced to simplify the derivation of the estimator. The estimator is calculated based on one J-spectral factorization for risk-seeking (θ<0) or one H2 spectral factorization for risk-averse (θ>0). A numerical example is given to demonstrate the applicability of the result. [Copyright &y& Elsevier]

In this paper, we derive the Stackelberg solution associated with a leader–follower rational expectations model. By solving the dynamic rational expectations optimization problem subject to forward and backward stochastic difference equations (FBSDEs), we obtain the Stackelberg strategy of the leader with an adapted open-loop information structure, in terms of the FBSDEs. Furthermore, we solve the associated FBSDEs by establishing a nonhomogeneous relationship between backward and forward stochastic processes. This leads to an explicit form of the Stackelberg strategy of the leader. [ABSTRACT FROM AUTHOR]

This paper investigates the decentralized linear quadratic optimization and stabilization problem for Itô systems, where the system's controller has two parts: the deterministic and random parts. Unlike previous works, with positive semi-definite weighting matrices, finite-horizon optimization and infinite-horizon stabilization problems are considered. The chief challenge lies in solving the forward and backward stochastic differential equations and selecting the Lyapunov function. The relationship between the forward and backward processes is established using a modified version of the four-step scheme combined with the information pattern of the problem. The equivalent condition for the optimization problem is obtained based on the Riccati differential equation. Besides, the necessary and sufficient conditions for the stabilization problem are presented using the Lyapunov function defined by the optimal cost function. Finally, numerical examples illustrate the validity of the presented strategies. [ABSTRACT FROM AUTHOR]

This paper is concerned with uniform stabilization and social optimality for general mean field linear–quadratic control systems, where subsystems are coupled via individual dynamics and costs, and the state weight is not assumed with the definiteness condition. For the finite-horizon problem, we first obtain a set of forward–backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback-type control by decoupling the FBSDEs. For the infinite-horizon problem, by using solutions to two Riccati equations, we design a set of decentralized control laws, which is further proved to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems in different cases, respectively. Finally, the proposed decentralized controls are compared to the asymptotic optimal strategies in previous works. [ABSTRACT FROM AUTHOR]

This paper is concerned with the linear quadratic decentralized control of forward and backward stochastic difference system (FBSDS) with multiplicative noises and nested asymmetric information. The main contribution is to give the equivalent condition for the solvability of the problem and the explicit decentralized optimal controllers in terms of Riccati equations. The key technology is solving the forward and backward stochastic difference equations with partial information derived from stochastic maximum principle. • LQ decentralized control of forward and backward stochastic difference system with nested asymmetric information. • Forward and backward stochastic difference equations with partial information. • Present solvability condition and explicitly decentralized optimal controllers of the problem. • Propose novel Riccati equations to solve forward and backward stochastic difference equations. [ABSTRACT FROM AUTHOR]

In classical mean field games, the asymptotically optimal decentralized strategies are concerned for large-population systems. The computational complexity is reduced but a relatively large optimality loss may be caused in small-population systems. This paper is concerned with the optimal decentralized strategies for finite-population discrete-time linear quadratic mean field games and social control problems. The weighting matrices in the cost function are not assumed to be definite. We adopt the conditional expectations to transform the forward–backward stochastic difference equations (FBSDEs) of the finite-population system into the mean field FBSDEs of a representative player. For the non-cooperative games, the solvability of decentralized Nash equilibria is characterized by the existence of a solution to a system of FBSDEs, together with a convexity condition. For the cooperative social control, the solvability of decentralized social optimal control is characterized by the existence of regular solutions to two Riccati equations. The proposed decentralized strategies are optimal in the case of finite-population, and also consistent with the classical asymptotic optimal strategies in the case of infinite-population. Therefore the computational complexity is significantly reduced without additional optimality loss. [ABSTRACT FROM AUTHOR]

In this paper, we study the exact controllability of forward and backward stochastic difference system (FBSDS) with multiplicative noise. Different from the standard system governed by forward stochastic difference equation (FSDE), the inclusion of both initial and terminal conditions in FBSDS complicates the solvability which also leads to the challenge of exact controllability. To overcome the difficulty, we transform the FBSDS into an equivalent backward stochastic difference equation. Accordingly, we derive both the necessary and sufficient Gramian matrix criterion and the Rank criterion for the exact controllability of FBSDS, which is the main contribution of the paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the consensus control problem for multi-agent systems with agents characterized by high-order linear continuous-time systems subject to communication delays between neighbouring nodes in the network. A new consensus protocol is proposed. It requires communication between neighbouring agents only at certain sampling points, rather than at all times. It is also unique in the sense that it is nonlinear in the continuous-time domain but linear when the agents are viewed in the sampled-data domain. Under the proposed consensus protocol, marginally stable multi-agent systems can reach consensus for any large delay. Unstable multi-agent systems achieve consensus when the time delay is within a certain range. Moreover, in the single-input case, we give an optimal control gain which yields the fastest consensus speed. The proposed technique is expected to pave a new way for new theoretical studies on network properties required for consensus control. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite horizon stabilization control for a class of discrete time stochastic systems subject to multiplicative noise and input delay. By constructing a new cost function, a complete solution to the problem of finite horizon stabilization is given for the first time based on previous work Zhang et al. (2015). It is shown that the system can be stabilized in the mean square sense with the receding horizon control (RHC) if and only if two new inequalities on the terminal weighting matrices are satisfied. Moreover, the two inequalities can be solved by using iterative algorithm. The explicit stabilizing controller is derived by solving a finite horizon optimal control problem. Simulations demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem for a class of general second-order multi-agent systems (MASs) with communication delay. We first consider the delay-free case and obtain a necessary and sufficient condition for consensus. Then, based on the obtained conditions for the delay-free case, we deduce an explicit formula for the delay margin of the consensus for the case with time delay using the relationship between the roots of the characteristic equation and the time delay parameter. In addition, we consider the special case where the second-order model is a double integrator. For this case, simpler consensus conditions under communication delay are provided. [ABSTRACT FROM AUTHOR]

We consider the design of an optimal collision-free sensor schedule for a number of sensors which monitor different linear dynamical systems correspondingly. At each time, only one of all the sensors can send its local estimate to the remote estimator. A preliminary work for the two-sensor scheduling case has been studied in the literature. The generalization into multiple-sensor scheduling case is shown to be nontrivial. We first find a necessary condition of the optimal solution which can significantly reduce the feasible optimal solution space without loss of performance. By modelling a finite-state Markov decision process (MDP) problem, we can numerically search an asymptotic periodic schedule which is proven to be optimal. Some simple but effective suboptimal schedules for any systems are proposed. We also find a lower bound of the optimal cost, which enables us to quantify the performance gap between any suboptimal schedule and an optimal one. [ABSTRACT FROM AUTHOR]

This paper is concerned with the mean-square stabilization problem for discrete-time networked control systems (NCSs). It is assumed that control signal is sent to plant over a lossy communication channel, where network-induced delay and packet dropout occur simultaneously. A necessary and sufficient stabilizing condition is developed in terms of the unique positive-definite solutions to some coupled algebraic Riccati equations (CAREs). The contributions of this paper are twofold. First, an existence theorem of the maximum packet dropout rate is proposed. Second, for one-dimensional single-input system and the decoupled multi-input system, it is shown that the NCS is stabilizable iff the network-induced delay and the packet dropout rate satisfy some simple algebraic inequalities. If the network-induced delay is known a priori, the maximum packet dropout rate is given explicitly in terms of network-induced delay and unstable eigenvalues of the system matrix. If the packet dropout rate is known a priori, the maximum allowable delay bound is also given explicitly. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the distributed consensus problem for linear discrete-time multi-agent systems with delays and noises in transmission channels. Due to the presence of noises and delays, existing techniques such as the lifting technique and the stochastic Lyapunov theory are no longer applicable to the analysis of consensus. In this paper, a novel technique is introduced to overcome the difficulties induced by the delays and noises. A consensus protocol with decaying gains satisfying persistence condition is adopted. Necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non-leader–follower and leader–follower cases under a fixed topology. Under dynamically switching topologies and randomly switching topologies, sufficient conditions for strong consensus and mean square consensus are also obtained. Numerical examples are given to demonstrate the effectiveness of the proposed protocols. [Copyright &y& Elsevier]