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This paper considers the rational expectations model with multiplicative noise and input delay, where the system dynamics rely on the conditional expectations of future states. The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model. In particular, we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case. The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

This paper focuses on linear-quadratic (LQ) optimal control for a class of systems governed by first-order hyperbolic partial differential equations (PDEs). Different from most of the previous works, an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems. The contributions of this paper consist of the following aspects: 1) The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method. 2) A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed. Meanwhile, the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations (FBPDEs). 3) The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented. It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case, but also support the existing operator results and give a more convenient form of computation.

In this article, the problem of distributed optimization with nonconvex objective functions is studied by employing a network of agents. Each agent only has access to a noisy estimate on the gradient of its own objective function, and can only communicate with its immediate neighbors via a time-varying directed graph. To handle this problem, a distributed stochastic gradient descent algorithm is adopted. Existing works on distributed algorithms involving stochastic gradients only provide convergence results in expectation. Different from them, we study the convergence of the algorithm in high probability, i.e., the asymptotic convergence rate of the algorithm is characterized by the natural logarithm of the failure probability's inverse. Under mild assumptions on the graph connectivity, we prove that for the general nonconvex objective function, the average of gradients' norm squared converges in high probability. Furthermore, we also consider the case where the objective function satisfies the Polyak–Łojasiewicz condition. In this case, the difference between the objective function and its minimum value converges in high probability, and the convergence rate is faster than that in the general nonconvex case. Finally, simulations are provided to demonstrate the effectiveness of our theoretical results.

In this article, we mainly study an integrated networked control system operating over multipath routing networks, where the delivered control signal in each path experiences both transmission delay and packet loss. These imperfections significantly compromise system performance and may even cause instability. For such a system, we derive, for the first time, the necessary and sufficient stabilization condition utilizing a delay-dependent algebraic Riccati equation. Different from many previous works, one significant contribution is that our control policy is designed as the feedback of an extended state that contains the current available state and relevant past control information. Furthermore, we introduce an existence and uniqueness theorem for the maximum packet loss rate in symmetric systems. Notably, we derive its closed-form expression specifically in the scalar case.

This article is concerned with linear quadratic regulation (LQR) and stabilization problems for discrete-time stochastic systems with multiple input channels and input delays. In comparison with single-input-channel problems, a key difficulty, induced by the different delays in different input channels, is that the information sets for multiple controllers are required to be asymmetric and coupled. A novel technique, referred to as orthogonal decomposition–reorganization, is proposed to conquer the coupling between channels. After the technique is used, a new method based on some refined decompositions is provided to solve the delayed forward–backward stochastic difference equations, which overcomes the asymmetry and amounts to finding the solvability condition of the underlying LQR problems. The complete solutions of the finite- and infinite-horizon LQR problems are given by newly developing Riccati-type equations. Also, a necessary and sufficient stabilizing condition is obtained for the system restricted by a performance index. Finally, the effectiveness of the results is evaluated by a numerical example.

This article investigates the stabilization and optimal control problems for Markov jump linear system (MJLS) with multiplicative noises and input delays. By overcoming the substantive difficulty resulting from the invalidity of the separation principle, we provide a complete solution to the addressed problems by means of 1) necessary and sufficient solvability, and the analytical formula on optimal finite horizon control in line with a generalized coupled difference Riccati equation; and 2) necessary and sufficient stabilizability, and the explicit expression of the optimal controller on infinite horizon according to a delayed generalized coupled algebraic Riccati equation (D-GCARE). It is shown that the MJLS with multiplicative noises and input delays is mean square stabilizable if and only if the D-GCARE has a specific solution. Our main results are attained through the creation of a novel delayed stochastic Markov maximum principle as well as the construction of a novel class of delayed Markov Lyapunov function.

This article studies the stabilization control of the Stackelberg game-based system (SGBS) which involves a leader and a follower under continuous time. There are two main contributions: first, the explicit Stackelberg strategy and the optimal performance index under finite horizon are derived based on Riccati equations (REs). Second, the equivalent condition for the SGBS to be stabilizable is obtained, meanwhile, the corresponding Stackelberg strategy and optimal index under this condition are given by REs. Different from the previous works, in the optimization process of the leader, we obtain the linear Stackelberg strategy based on state feedback by applying the matrix maximum principle. Our key technique is solving forward–backward differential equations obtained from the maximum principle.

This brief studies the mean-square consensus problem for discrete-time heterogeneous multi-agent systems, where the state information is received with varying dropout uncertainty, which leads to heterogeneous observations. The main challenge addressed in this brief is the design of the state estimator and the controller for each agent with different dynamics subject to multiplicative noise. The optimal estimator is designed based on the measurement value to estimate each agent’s state, and a novel distributed dynamic output feedback control protocol is first developed based on the given estimator. A sufficient solvability condition for achieving mean-square consensus in heterogeneous multi-agent systems is derived. Finally, simulation results show the effectiveness of the proposed control strategy.

In this article, we consider the discrete-time rational expectations model with state delays. In particular, the dynamic equation relies both on the history of states and the conditional expectation of the future states. The novelty of this article lies in transforming the solvability of the rational expectations model to that of the forward and backward stochastic difference equations (FBSDEs). The main contribution is to obtain the (unique) solvability and the explicit solutions for the FBSDEs in both finite horizon and infinite horizon. This accordingly gives the explicit solution of the rational expectations model. The key technology is to establish a nonhomogeneous relationship between forward and backward processes of the FBSDEs.

This article considers the decentralized linear–quadratic–Gaussian control problem for discrete-time decentralized system controlled by two players. In this scenario, player 1 shares a unit delayed observations and control inputs with the controller of player 2, whereas due to the limiting capacity, the controller of player 1 cannot obtain the observations and control inputs of player 2, which leads to the asymmetric one-step delay information. It should be emphasized that this structure makes the classical separation principle fail. Under the assumption of linear control strategies, we derive the optimal estimators based on asymmetric information. In virtue of the Pontryagin's maximum principle, the optimal explicit decentralized controllers are obtained by solving the forward and backward stochastic difference equations. It is noted that the control gains are coupled with the estimation gains. Moreover, the estimation gains satisfy the forward Riccati equations and the control gains follow the backward Riccati equations, which cannot be solved simultaneously. To this end, we present iterative solutions to the coupled forward and backward Riccati equations. Finally, a sufficient condition for the stabilization problem is given in terms of the coupled algebraic Riccati equations. Numerical examples are illustrated to show the effectiveness of the proposed algorithm.

This article aims to solve the multiobjective optimization control problem by investigating the consensus problem of multiagent simultaneous optimization with state and control dependent multiplicative noise. The main contributions of this work are two-fold. First, the optimal consensus control problem is solved by designing the free item of an optimal controller, and the coefficient of the feedback gain is obtained based on analyzing a parameterized generalized algebraic Riccati equation. Second, we derive a new consensus controller that comprises two parts different from the current consensus. One part minimizes a linear quadratic index with a singular control weighting matrix, and the other affords the multiagent systems to achieve mean square consensus.

A stabilization problem for stochastic systems with multiple input delays is investigated herein. A new method to construct an optimal control problem with input constraints is adopted. A sufficient stabilization condition is established via Riccati-type equations, whose verification is computationally simple because the variable dimension of the equations does not increase with regard to the delay. A stabilization controller is proposed, and it is a feedback of the state and a history input. This controller uses less history information than those with distributed terms. Two numerical examples illustrate the effectiveness of the obtained results.

We investigate the linear quadratic Gaussian–Stackelberg game under a class of nested observation information patterns. The follower uses its observation data to design its strategy, whereas the leader implements its strategy using global observation data. We show that the solution requires solving a new type of forward–backward stochastic differential equation, whose drift components contain two conditional expectation terms associated with the adjoint variables. We then propose a method to find the functional relations between each adjoint pair, i.e., each pair formed by an adjoint variable and the conditional expectation of its associated state. The proposed method follows a layered pattern. More precisely, in the inner layer, we seek the functional relation for the adjoint pair under the sigma-subalgebra generated by follower's observation information, and in the outer layer, we look for the functional relation for the adjoint pair under the sigma-subalgebra generated by leader's observation information. Our result shows that the optimal open-loop solution admits an explicit feedback type representation.

Gas turbine engines must be operated by means of control, and how to achieve multivariable control decoupling with aero-engine control constraints is an open thorny issue attracting increasingly more attention. The paper considers the multivariable decoupling problems of aero-engines by using a compound controller, which originates from the fact that it is impossible to eliminate all the nonlinear dynamics of system to obtain desired constant linear closed-loop system by using full actuated control because of modeling errors and some physical constraints. Two controllers are involved in the compound controller. One is a fully actuated controller and the other is classical feedback controller. In order to use fully actuated control and maintain the accuracy of engine model, a full state scheduling linear parameter-varying (LPV) modeling method is proposed based on fuzzy neural network weights. For a general input matrix of the system, its generalized inverse is applied to design fully actuated controller to result in a pseudolinear system. Combined with a feedback controller and control limiter, the control synthesis is achieved. The simulation shows that the proposed method is possessed of a better decoupling and tracking effect compared with traditional control approach.

In this article, we study a class of discrete-time decentralized linear-quadratic-Gaussian (LQG) control problems with two controllers and $d$-step delayed information sharing pattern. An explicit form of the pair of optimal linear controllers is obtained in terms of backward Riccati equations and forward equations of estimation error covariance. To overcome the difficulty that arises due to the coupling of the backward–forward equations, we propose a forward iteration approach to derive a steady-state solution. This accordingly leads to an asymptotically optimal linear controller where the feedback gains are designed by using the convergent steady-state solutions.

This paper studies the decentralized open-loop asymptotic Nash equilibria for linear quadratic mean field games following the direct approach. In the first step of the direct approach, the necessary and sufficient condition for the existence of centralized open-loop Nash equilibria is obtained by using the variational analysis. The Nash equilibria are characterized by an adapted solution to a system of forward-backward stochastic differential equations. A feedback representation of the open-loop Nash equilibrium is obtained by using the solution to a system of Riccati equations. In the second step of the direct approach, the decentralized asymptotic Nash equilibria are designed by considering the limit of the centralized Nash equilibria with a standard Riccati equation and a non-symmetric Riccati equation. The results show that the decentralized open-loop asymptotic Nash equilibria coincide with the feedback solutions which are designed by the fixed-point approach, provided both exist.

This brief is concerned with the feedback Nash equilibrium for networked control systems (NCSs) with packet dropouts. The packet dropouts occur when the state information is transformed via a wireless network, causing the fall that the state information is unavailable to design the feedback Nash equilibrium. The main contribution of this brief is that the necessary and sufficient condition for the existence of feedback Nash equilibrium is presented. The key is that by decoupling solving the forward and backward difference equations (FBDEs), the analytical solutions of the two controllers are given in terms of the two coupled Riccati equations.

We address forward–backward stochastic differential equations (FBSDEs) with random coefficients. Differently from previous approaches, we consider FBSDEs with coefficients that are random and correlated with forward and backward variables. In addition, expectation terms appear in the forward equation, and this makes challenging to solve coupled FBSDEs, e.g., those coming from corporations’ fiscal policy planning. Using a discretization approach, an analytic solution to the FBSDEs is given in terms of coupled stochastic Riccati-type differential equations. We also apply our results to optimal deterministic control problem for Itô stochastic systems with both random and deterministic coefficients. Our results show that the discretization approach is a powerful tool to decouple complex FBSDEs.

This article considers the decentralized linear–quadratic (LQ) optimal control problem for the multiplicative-noise stochastic systems in discrete time with asymmetric information. There exist two controllers in the system, and each controller has its own information in general structure. The adopted information structure is adapted open loop for both controllers. The main contribution is to derive the necessary and sufficient condition for the unique solvability of the LQ control problem with a general asymmetric information structure and present the explicitly optimal controllers in terms of the proposed Riccati equations. The key is to explicitly solve the forward and backward stochastic difference equations, which are derived from the maximum principle.

This paper is concerned with linear forward–backward stochastic differential equations (FBSDEs) with state delay, the solvability which is much more complex than the case of no delay or input delay caused by the prediction of the backward processes of the future time. To overcome this difficulty, we innovatively establish the non-homogeneous relationship between the backward and forward processes with the help of the corresponding discrete-time system. The main contribution is to give the explicit solution to the FBSDEs with state delay in terms of partial Riccati equations for the first time. The presented results form the basis to solve the challenging problem of linear quadratic optimal control for multiplicative-noise stochastic systems with state delay.

The paper considers the linear quadratic regulation (LQR) and stabilization problems for Ito stochastic systems with two input channels of which one has input delay. The underlying problem actually falls into the field of asymmetric information control because of the nonidentical measurability induced by the input delay. In contrast with single-channel single-delay problems, the challenge of the problems under study lies in the interaction between the two channels which are measurable with respect to different filtrations. The key techniques conquering such difficulty are the stochastic maximum principle and the orthogonal decomposition and reorganization technique proposed in a companion paper. The authors provide a way to solve the delayed forward backward stochastic differential equation (D-FBSDE) arising from the maximum principle. The necessary and sufficient solvability condition and the optimal controller for the LQR problem are given in terms of a new Riccati differential equation established herein. Further, the necessary and sufficient stabilization condition in the mean square sense is provided and the optimal controller is given. The idea proposed in the paper can be extended to solve related control problems for stochastic systems with multiple input channels and multiple delays.

In this article, we characterize the joint effects of plant uncertainty, transmission delay, and fading channel on the stabilization problem of networked control systems (NCSs). We assume that the controller remotely controls the plant and the control packet is transmitted over a delayed and fading channel. We formulate the integrated system as an uncertain discrete-time stochastic system with both input delay and multiplicative noise. The innovative contributions of this article are described as follows. We propose a set of necessary and sufficient conditions for stabilizing an uncertain-free system. Moreover, for the general uncertain model, we derive the necessary and sufficient stabilization condition in terms of symmetric matrix homogeneous polynomials, which can be verified by linear matrix inequality (LMI) feasibility test. As an application, under the parallel transmission strategy, we derive an explicit formula for computing the maximum allowable delay bound, which is uniquely determined by system parameters and signal-to-noise ratio.

Linear quadratic regulation (LQR) is very fundamental in modern control theory. The theory has been developing for several decades. However, the LQR problem for stochastic systems with input delays still remains outstanding. The paper focuses on the LQR problem for Ito stochastic systems with two control channels and a delay, which will pave a way to approach the corresponding H∞control problem. In contrast with the single channel problem, this problem is more typical and involved since the two channels problem actually encounters interaction between channels besides the delay. The paper focuses on providing a necessary and sufficient solvability condition and optimal control. The sufficiency is proved by finding a suitable value functional and completing the square. The necessary condition is obtained by the variant of the calculus of variations. What’s more important, due to that the result is given based on coupling ordinary and partial differential equations, we present the analytic solution to these equations. The idea is also suitable for handling the LQR problem for Ito stochastic systems with multiple control channels and multiple delays.

This article considers the optimal control and stabilization problems for networked control systems (NCSs) with asymmetric information. In this NCSs model, the remote controller can receive packet-dropout states of the plant, and the available information for the embedded controller are observations of states and packet-dropout states sent from the remote controller. The two controllers operate the plant simultaneously to make the quadratic performance minimized and stabilize the linear plant. For the finite-horizon case, since states of the plant cannot be obtained perfectly, we develop the optimal estimators for the embedded and remote controllers based on asymmetric information, respectively. Then we give the necessary and sufficient condition for the optimal control based on the solution to the forward–backward stochastic difference equations. For the infinite-horizon case, it is shown that the system is bounded in the mean-square sense if and only if there exist the solutions to the two coupled algebraic Riccati equations and the packet-dropout probability satisfies certain condition. Numerical examples on the unmanned underwater vehicle are presented to show the effectiveness of the given algorithm.

This paper studies the mixed H2/H∞control for continuous-time linear dynamic systems. By applying Stackelberg game approach, the control input is treated as the leader and the disturbance is treated as the follower, respectively. Under standard assumptions and maximum principle, a necessary and sufficient existence condition which is based on three decoupled Riccati equations is obtained. Explicit expression of controllers and solutions to forward backward differential equations (FBDES) are obtained by homogeneous analysis of variables. A numerical example is finally given to verify the efficiency of the proposed approach.

In this paper, we consider the decentralized optimal control problem for linear discrete-time systems with multiple input channels. First, under centralized control, the optimal feedback gains are given in terms of two algebraic Riccati equations. A reduced order observer is then designed using only the local input and output information. By selecting an appropriate initial value for the observer, we derive an observer-based decentralized optimal controller where the feedback gain is the same as that obtained in the centralized optimal control problem. Last but not least, we study the optimal control problem of non-homogeneous multi-agent systems as an application. A suboptimal decentralized controller is obtained and the difference between the suboptimal cost and the optimal one is given.

We consider the achievable delay margin of a real rational and strictly proper plant, with unstable complex poles, by a linear time-invariant (LTI) controller. The delay margin is defined as the largest time delay such that, for any delay less than this value, the closed-loop stability is maintained. Drawing upon a frequency domain method, particularly a bilinear transform technique, we provide an upper bound of the delay margin, which requires computing the maximum of a one-variable function. Finally, the effectiveness of the theoretical results is demonstrated through a numerical example.

This paper investigates a consensus problem for multiagent systems with both system and measurement noises. By applying Kalman filtering and weighted-average estimation fusion, a novel consensus protocol is designed based on distributed state estimation. It is shown that under the proposed protocol, the consensus error is bounded and can be exactly characterized via the solution to a Lyapunov equation. The numerical examples are given to show the correctness of the proposed results.

This paper is concerned with the mixed H2/H∞control with linear continuous time system and time delay. To deal with this, we presents a Stackelberg strategy by treating the control input and the disturbance as leader and follower, respectively. The leader’s control strategy minimizes the cost function which is in H2norm and the follower’s control strategy maximizes the cost function which is in H∞norm. The main technique of this paper is deal with the noncausal relationship of the variables caused by time delay in the control input by introducing two costates to capture the future information and one state to capture the past information. Through theory analyzing, the Stackelberg strategy exists uniquely. Moreover, with the assistance of the extended state space expression, the explicit expression of the strategy is obtained.

This paper considers the output feedback control and stabilization problems for network control systems (NCSs) with packet dropout and input delay, and the TCP (transmission control protocol) case is mainly investigated. Specifically, whether the control signal is lost can be acknowledged by the receiver in the NCSs. The main contributions are: 1) For the finite horizon case, the “optimal” output feedback control is derived by using the dynamic programming approach, and it is noted that the separation principle holds for the considered situation; 2) For the infinite horizon case, for the first time, the necessary and sufficient stabilization conditions are derived for NCSs with packet dropout and delay.

This paper is mainly concerned with the time-inconsistent stochastic linear quadratic (LQ) control problem in a more general formulation for discrete-time systems. The time-inconsistency arises from three aspects: the coefficient matrices depending on the initial pair, the terminal of the cost function involving the initial pair together with the nonlinear terms of the conditional expectation. The main contributions are: firstly, the maximum principle is derived by using variational methods, which forms a flow of forward and backward stochastic difference equations (FBSDE); secondly, in the case of the system state being one-dimensional, the equilibrium control is obtained by solving the FBSDE with feedback gain based on several nonsymmetric Riccati equations; finally, the necessary and sufficient solvability condition for the time-inconsistent LQ control problem is presented explicitly. The key techniques adopted are the maximum principle and the solution to the FBSDE developed in this paper.

In this study, consensus problem for general high-order multi-agent systems with communication delay is investigated. Given the unstable agent dynamics and a known communication delay, two consensus protocols are designed to guarantee consensus over undirected network. By jointly researching the effects of agent dynamics and network topology, allowable delay bounds depending on the maxima of concave functions are easy to calculate. Especially, the maximum delay bound is derived when the network topology is completely connected. The main approach for the same involves designing the control gains on the basis of the solution of a parametric algebraic Riccati equation. Finally, the theoretical results are demonstrated via numerical simulations.

The stabilization with receding horizon control (RHC) of Itô stochastic time-varying systems is studied in this paper. Based on monotonically non-increasing of optimal cost and stochastic Lyapunov stability theory, a necessary and sufficient stabilization condition on the terminal weighting matrix is proposed, which guarantees the mean-square stability of the closed-loop system. The explicit receding horizon controller is obtained by employing stochastic maximum principle. Simulations demonstrate the effectiveness of the proposed method.

This paper considers the linear quadratic Gaussian (LQG) control problem for discrete-time systems subject to multiplicative noises and input delay. When the state variables can be obtained exactly, the necessary and sufficient condition for the existence of a unique solution to the LQG control has been presented and an explicit analytical expression is given for the optimal LQG controller. More specially, the optimal LQG controller is derived which consists of the feedback form of the conditional expectation of the state and one additive deterministic term based on the coupled Riccati equations. Through the completing square approach, the optimal controller is obtained based on the solution to the forward and backward stochastic difference equations (FBSDEs).

Different from previous works, this paper will provide the necessary and sufficient (essential) solution to linear quadratic (LQ) optimal control problem for continuous-time mean-field systems. Firstly by applying the Maximum Principle developed in this paper, the necessary and sufficient solvability condition of the finite horizon mean-field optimal control problem is presented in an explicit expression form (in analytical form) for the first time, which is completely different from the operator-type conditions obtained in previous works. Secondly, we explore the analytical solution to the forward and backward stochastic differential equation (FBSDE) of the mean-field optimal control problem. Accordingly, the optimal controller, in terms of system state and its expectation, is designed via a coupled Riccati equation. It is very interesting to show that the coupled Riccati equation is derived from the solution to the FBSDE, which has the similarity with the case of standard optimal control.

This paper considers the stochastic linear quadratic regulation (LQR) problem for Itô stochastic systems with multiple input controllers. The explicit controllers are given in terms of two Riccati equations by introducing one new costate and establishing the homogeneous relationship between the state and the new costate. More importantly, it is more computation saving for the derived Riccati equations than the one derived by augmentation technique.

A newly proposed distributed dynamic state estimation algorithm based on the maximum a posteriori (MAP) technique is generalised and studied for power systems. The system model involves linear time-varying load dynamics and nonlinear measurements. The main contribution of this paper is to compare the performance and feasibility of this distributed algorithm with several existing distributed state estimation algorithms in the literature. Simulations are tested on the IEEE 39-bus and 118-bus systems under various operating conditions. The results show that this distributed algorithm performs better than distributed quasi-steady state estimation algorithms which do not use the load dynamic model. The results also show that the performance of this distributed method is very close to that by the centralized state estimation method. The merits of this algorithm over the centralized method lie in its low computational complexity and low communication load. Hence, the analysis supports the efficiency and benefits of the distributed algorithm in applications to large-scale power systems.

This paper considers the distributed control of the LQR problem for discrete-time multiagent systems. Distributed controllers are designed based on the solutions of centralized optimal control and the topological structure of the systems. Under mild conditions, it is shown that the distributed controller can approximate to the centralized optimal controller. Then the states of the closed-loop systems of the distributed control exponentially converge to the states of the closed-loop systems of the centralized optimal control. Some examples are given to show effectiveness of the proposed results.

This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon approach. The explicit time-varying controller is designed if the condition is satisfied. The presented results are new to the best of our knowledge.

This paper addresses the node localizability problem in 2-D, aiming at determining which nodes are localizable in a sensor network with internode distance measurements. Toward this objective, a sequential cluster-based approach is proposed. The idea is to expand the set of localizable nodes starting from the set of anchor nodes cluster by cluster rather than node by node. Taking computation efficiency in practice into account, we consider the size of a cluster up to four nodes each time. Then, we develop a necessary and sufficient condition to determine whether a cluster up to four nodes is jointly localizable given the distance measurements among them and the distance measurements between them and their neighbors with known coordinates. In terms of this necessary and sufficient condition, both centralized and distributed algorithms are developed for detecting localizable nodes in a given sensor network. It is demonstrated that our approach outperforms well-known techniques, such as trilateration, bilatration, and wheel extension in finding as many localizable nodes as possible.

In this paper, the linear quadratic regulation problem for discrete-time systems with state delays and multiplicative noise is considered. The necessary and sufficient condition for the problem admitting a unique solution is given. Under this condition, the optimal feedback control and the optimal cost are presented via a set of coupled difference equations. Our approach is based on the maximum principle. The key technique is to establish relations between the costate and the state.

This paper studies the consensus problem for discrete-time multi-agent systems of first-order in the presence of constant communication delay. Provided that the agent dynamics is unstable and the network topology is undirected, effects of two kinds of communication delays on consensus are investigated. When the relative information is affected by delay, we show that the effect of delay can be alleviated by using the historical input information in the protocol design. On the other hand, if the communication delay only influences the actually transmitted information, sufficient condition admitting any large yet bounded delay for consensus is obtained, and the delay in this case is allowed to be unknown and time-varying. Finally, simulation results are provided to demonstrate the effectiveness of the theoretical results.

This paper investigates a consensus design problem for continuous-time first-order multiagent systems with uniform constant communication delay. Provided that the agent dynamic is unstable and the diagraph is undirected, sufficient conditions are derived to guarantee consensus. The key technique is the adoption of historical input information in the protocol. Especially, when agent’s own historical input information is used in the protocol design, the consensus condition is constructed in terms of agent dynamic, communication delay, and the eigenratio of the network topology. Simulation result is presented to validate the effectiveness of the theoretical result.

Abstract: This paper is concerned with the l 2–l ∞ filtering problem for a class of piecewise discrete-time linear systems. Attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the l 2–l ∞ sense. By using the piecewise Lyapunov function, a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities (LMIs). It has been shown that the l 2–l ∞ filtering problem can be solved as an LMI optimization problem. Two numerical examples are presented to demonstrate the validity of the proposed design method.

This paper is concerned with the infinite horizon linear quadratic optimal control for discrete‐time stochastic systems with both state and control‐dependent noise. Under assumptions of stabilization and exact observability, it is shown that the optimal control law and optimal value exist, and the properties of the associated discrete generalized algebraic Riccati equation (GARE) are also discussed. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

This paper investigates the robust H∞control problem for continuous‐time piecewise time‐delay systems by using piecewise continuous Lyapunov function. The uncertainties of the systems under consideration are expressed in a linear fractional form. A strict linear matrix inequality approach is developed to obtain delay‐dependent asymptotic stability conditions and H∞performance. The H∞controller design problem is solved by exploiting the cone complementarity linearization (CCL) method. Finally an example is given to illustrate the application of the proposed approach. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society