Optimal Control for Discrete-time NCSs with Input Delay and Markovian Packet Losses: Hold-Input Case

TL;DR

This paper develops a novel optimal control framework for discrete-time networked control systems with input delay and Markovian packet losses, using hold-input strategies and coupled Riccati equations to ensure stability and optimality.

Contribution

It introduces necessary and sufficient conditions for optimal control with hold-input strategy under input delay and Markovian losses, addressing computational complexity and stability.

Findings

Derived coupled Riccati-type equations for finite horizon optimal control.

Established mean-square stability conditions via algebraic Riccati equations.

Addressed forward-backward difference equations with adaptive controllers.

Abstract

This paper is concerned with the linear quadratic optimal control problem for networked system simultaneously with input delay and Markovian dropout. Different from the results in the literature, we consider the hold-input strategy, which is much more computationally complicated than zero-input strategy, but much better in most cases especially in the transition phase. Necessary and sufficient conditions for the solvability of optimal control problem over a finite horizon are given by the coupled difference Riccati-type equations. Moreover, the networked control system is mean-square stability if and only if the coupled algebraic Riccati-type equations have a particular solution. The key technique in this paper is to tackle the forward and backward difference equations, which are more difficult to be dealt with, due to the adaptability of controller and the temporal correlation caused by simultaneous input delay and Markovian jump.