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In this paper, we are concerned with the stabilization problem of the game-based control system. In particular, two players are involved in the system where one is to minimize the related cost function and the other is to stabilize the system. Different from the previous works, the new contribution is to derive the necessary and sufficient condition for the stabilization of the game-based control system by applying Stackelberg game method. The key technique is to explicitly solve the forward and backward difference equations (FBDEs) from the Stackelberg game and give the optimal feedback gain matrix of the leader by using the matrix maximum principle. [ABSTRACT FROM AUTHOR]

The linear quadratic regulation (LQR) problem for discrete-time networked control systems (NCSs) is investigated in this article. The difference from most previous works is that input delay and packet losses occur simultaneously in the communication channel connecting the controller to the actuator. Moreover, the data packet dropout is modeled as a time-homogeneous Markov process which poses challenges due to the temporal correlation. The contributions of this article are twofold. First, by applying the maximum principle involving Markov jumps and delay, the linear quadratic optimal control problem in finite horizon is solved and the solution is given in terms of a forward and a backward stochastic difference equations (FBSDEs-M). Second, under a basic assumption, the infinite horizon optimal control problem is solved and the necessary and sufficient condition for mean square stabilization is given in terms of the solutions to coupled algebraic Riccati-type equations with Markov jumps. The presented results are new to the best of our knowledge since there is no existing work that tackles delay and Markovian packet dropouts simultaneously. It is a generalization of the previous work in which the packet dropouts is modeled as an independent identically distributed Bernoulli process. [ABSTRACT FROM AUTHOR]

In this paper, a delay-dependent algebraic Riccati equation (DARE) approach is developed to study the mean-square stabilization problem for continuous-time networked control systems. Different from most previous studies that information transmission can be performed with zero delay and infinite precision, this paper presents a basic constraint that the designed control signal is transmitted over a delayed communication channel, where signal attenuation and transmission delay occur simultaneously. The innovative contributions of this paper are threefold. First, we propose a necessary and sufficient stabilizing condition in terms of a unique positive definite solution to a DARE with ${Q>0}$ and ${R>0}$. In accordance with this result, we derive the Lyapunov/spectrum stabilizing criterion. Second, we apply the operator spectrum theory to study the stabilizing solution to a more general DARE with ${Q\geq 0}$ and ${R>0}$. By defining a delay-dependent Lyapunov operator, we propose the existence theorem of the unique stabilizing solution. It is shown that the stabilizing solution, if it exists, is unique and coincides with a maximal solution. Third, as an application, we derive the explicit maximal allowable delay bound for a scalar system. To confirm the validity of our theoretic results, two illustrative examples are included in this paper. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the optimal output feedback control and stabilization problems for discrete-time multiplicative noise system with intermittent observations. The main contributions of this paper can be concluded as follows. First, different from the previous literatures, this paper overcomes the barrier of the celebrated separation principle for stochastic control problems of multiplicative noise systems. Based on the measurement process, the optimal estimation is presented, and by using dynamic programming principle, the optimal output feedback controller is designed with feedback gain based on the given coupled Riccati equations. Second, the necessary and sufficient stabilization conditions for multiplicative noise system with intermittent observation in the mean square sense are developed for the first time. Finally, the novel results developed in this paper can be applied to solve the output feedback control and stabilization problems for general networked control system of user datagram protocol network case. The range of packet losses rate and the allowable maximum packet losses rate are presented explicitly. [ABSTRACT FROM AUTHOR]

This brief is concerned with the control problem for discrete-time networked control systems. It is assumed that state and control signals transmit through an unreliable communication channel, where packet dropout and input delay occur simultaneously. The main contributions are twofold. First, we obtain the optimal LQR controller, which is a linear function of the optimal state estimator, with the feedback gain based on a standard difference Riccati equation. It is noted that the state estimator and the controller can be calculated separately. Second, a necessary and sufficient condition for the mean-square stabilization is derived. It should be stressed that the eigenvalues of the system matrix and the packet dropout probability determine the stabilizing condition, which is uncorrelated with input delay. [ABSTRACT FROM PUBLISHER]

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 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 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]

This paper is concerned with the linear–quadratic optimal control problem for networked systems simultaneously with input delay and Markovian packet losses under hold-input compensation strategy, which is different from the literature. Necessary and sufficient conditions for the solvability of optimal control problem over a finite horizon are given by coupled difference Riccati-type equations. Moreover, the networked control system is mean-square stability if and only if coupled algebraic Riccati-type equations have a particular solution. Due to input delay and Markovian packet dropout, it leads to the failure of the separation principle, which is a fundamental obstacle. The key technique in this paper is to tackle forward and backward difference equations by decoupling. [ABSTRACT FROM AUTHOR]