Receding horizon control for discrete‐time multiple input delay systems

Abstract

Summary This paper is concerned with stabilization problem for discrete‐time systems with multiple input delay. By defining a new cost function, the stabilization condition is derived based on monotonically nonincreasing of the optimal cost. It is shown that if the 2 weighting matrices in the cost function satisfy the given linear matrix inequality, receding horizon controller can stabilize the input delay systems. Moreover, the explicit stabilization controller with the new cost function is obtained by solving a finite horizon optimal control problem. A numerical example illustrates the effectiveness of the proposed method.

Distributed RHC stabilization for discrete‐time large‐scale systems with imposed constraints

“…Lemma 3. Given Q > 0, R > 0, suppose that imposed constraint discrete-time large-scale systems (1) can be stabilized by RHC, then the following coupled Lyapunov equations (20)- (21) admit a solution with P > 0,P + P > 0:…”

“…Necessity: Suppose imposed constraint discrete-time large-scale systems (1) can be stabilized with the RHC. According to Lemma 3, the coupled Lyapunov equation admits a solution with P > 0,P + P > 0, there exist Θ 1 = −H −1 N, Θ 2 =F − Θ 1 such that (20)- (21) holds. This is the end of the proof.…”

“…In this paper, we refer to the methods in our other works using RHC to stabilize subsystems and proposed a new method of distributed RHC. We are concerned with the stabilization problem of distributed RHC for a class of discrete‐time large‐scale systems with constraints.…”

Receding Horizon Control-Based Stabilization of Discrete-Time Stochastic Systems With State Delay

“…The RHC stabilization problem of a discrete-time stochastic system with single input delays was studied in [22], the necessary and sufficient conditions were developed with the form of Lyapunov type inequality. Reference [23] studied the system with multiple input delay, the sufficient stabilization condition was obtained. For the system with state delay, the linear quadratic optimal control problem of a discrete-time stochastic system was settled in [24], but the stabilization problem has not been concerned.…”

“…In this paper, we discuss the RHC stabilization of discretetime stochastic system with state delay. The main contributions of this paper are summarized as follows: (1) motivated by [23], [24], a conditional expectation type cost function is constructed in order to obtain the stabilizing conditions;…”