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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.

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 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.

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 technical note focuses on optimal filtering for It\mathhato stochastic continuous-time systems with multiple delayed measurements. Stochastic analysis and calculus of stochastic variables are the main tools employed for the analysis and design. For an It\mathhato-stochastic system, its stochastic differential and integral have a significant place and are different from that for other stochastic systems owing to the Wiener or the Brownian process. In this technical note, an It\mathhato stochastic continuous-time system with multiple delayed measurements is first reduced to an equivalent system with delay free measurements by solving stochastic equation via the non-singularity of the transition matrix instead of reorganizing the innovation. Then, based on the delay-free measurements the optimal filter is derived through calculation of the conditional expectation. It is should be stressed that the optimal filter follows directly from the manipulation of the performance. Finally, a short interest rate model in mathematical finance is chosen to demonstrate the design of the optimal filter via the approach proposed in the technical note. [ABSTRACT FROM PUBLISHER]

In this note, we study the consensus problem for multiagent systems with measurement noises. Different from the existing approach, the consensus problem is converted to a root finding problem for which the stochastic approximation theory can be applied. By choosing an appropriate regression function, we propose a consensus algorithm which is applicable to systems with more general measurement noise processes, including stationary autoregressive and moving average (ARMA) processes and infinite moving average (MA) processes. Further, we establish a relationship between the convergence rate and the exponent of the step size of the algorithm. Particularly, strong convergence rate for systems with a leader-follower topology is studied. [ABSTRACT FROM AUTHOR]

We consider remote state estimation over a packet-dropping network. A new suboptimal filter is derived by minimizing the mean squared estimation error. The estimator is designed by solving one deterministic Riccati equation. Convergence of the estimation error covariance and mean square stability of the estimator are proved under standard assumptions. It is shown that the new estimator has smaller error covariance and has wider applications when compared with the linear minimum mean squared error estimator. One of the key techniques adopted in this technical note is the introduction of the innovation sequence for the multiplicative noise systems. [ABSTRACT FROM PUBLISHER]