Control for Multiplicative Noise Systems With Packet Losses and Measurement Delays

Chuanzhi Lv,Xiao Liang,Haixia Wang,Xiao Lu

doi:10.1109/access.2020.3025094

Abstract

This paper mainly considers the control problems for discrete-time multiplicative noise systems with packet losses and measurement delays. The main contributions are two-fold. Firstly, based on Pontryagin’s maximum principle, the optimal output feedback controller is obtained. Secondly, a necessary and sufficient stabilization condition for multiplicative noise systems is derived in terms of the coupled algebraic Riccati equations. Moreover, it has been proved that the stabilization condition only depends on the eigenvalue of the system matrix and the probability of packet losses which is not related to measurement delays.

Highlights

Modern control theory is based on state variables that are whole description for the system and are usually not measurable
In virtue of a Lyapunov function defined with the optimal cost function, we show that the system is mean square stable if and only if the coupled algebraic Riccati equations (AREs) have a unique specific solution
This paper aims to analyse the problem of output feedback control and stabilization for multiplicative noise systems with packet dropouts and measurement delays

Summary

INTRODUCTION

Modern control theory is based on state variables that are whole description for the system and are usually not measurable. To the best of our knowledge, there is seldom process on the complete solution to the problem of optimal output feedback control for multiplicative noise systems with both measurement packet losses and delays. Theorem 1: Problem 1 has a unique solution if and only if Hk >0 for θ ≤ k ≤ N If this condition holds, the optimal output feedback controller designed to minimized (4) is given by uk = − k xk/k , k = θ, . The problem under consideration can be described as follows: Problem 2: Find the F(yk )-measurement output feedback controller uk to stabilize system (2) in the mean square sense, and to minimize infinite horizon cost function (27)

SOLUTION TO PROBLEM 2

NUMERICAL EXAMPLES

CONCLUSION