An Output Feedback Predictive Control for Stochastic Stabilization of a System With Multiple Fixed State Delays and Multiple Markov Input Delays

Janghoon Yang

doi:10.1109/access.2020.2997684

Abstract

This paper studies the stochastic stabilization with an output feedback predictive control for a linear system with multiple fixed state delays and multiple Markov input delays. The two equivalent systems are developed through two steps. The original system is transformed to a system with augmented states in a state delay free form. Then, it is further transformed into a system with a predictive state in an input delay free form. The stochastic stability condition of the equivalent system is shown to be a sufficient condition for the stochastic stability of the original system. The stability condition is given as a set of linear matrix inequalities of which matrix size depends only on the maximum state delay, not on the maximum input delay. Simulation results show that the proposed methods provide similar or better performance than the conventional method while their complexities are much smaller in most cases.

Highlights

With the evolution of the internet, everything is being connected
While a delay can be harnessed to stabilization with articulated modeling [3], ignoring delay can be very detrimental to some control systems [4]
In this paper, we proposed two methods for designing a predictive output feedback controller to achieve stochastic stability

Summary

INTRODUCTION

With the evolution of the internet, everything is being connected. Widespread use of networks has made cyber-physical systems (CPS) and associated control methods more important than ever [1]. A conventional approach for the stabilization of a system with a Markov delay transforms it into an equivalent Markovian jump linear system (MJLS) with augmented states in a delay-free form of which dynamic system matrix follows a Markov process [15]. The Lyapunov-Krasovskii(LK) functional and integral inequality was exploited to derive a delay dependent stabilization condition for a state feedback control system when a state delay and an input delay were time varying [29]. Two predictive controls for a system with multiple fixed state delays and multiple Markov delays are developed from the sufficient conditions for the stabilization of equivalent systems without a delay. To derive the proposed predictive control methods, the conventional equivalent system model with state augmentation is exploited first to make it without state delays. It is noted that the control input depends on the history of sensor output due to the state delays and history of control input due to the input delays

THE SECOND METHOD

ALGORITHM IMPLEMENTATION

NUMERICAL SIMULATIONS

CONCLUSIONS