Observer‐based tracking control for switched stochastic systems based on a hybrid 2‐D model

Abstract

Summary This paper is concerned with the observer‐based output tracking problem for a class of linear switched stochastic systems with time delay and disturbance by using repetitive control approach. More precisely, a two‐dimensional hybrid model is incorporated to obtain and optimize the repetitive controller. In particular, the repetitive controller is used to improve the tracking performance through its continuous learning actions. In addition, an equivalent‐input‐disturbance estimator is incorporated into the repetitive control design approach to reduce the effect of the external disturbances. The main aim of the control design is to track the periodic reference signal with the measured output of the system under consideration even in the presence of an unknown bounded disturbance. By constructing a suitable Lyapunov‐Krasovskii functional and using average dwell time approach and Jensen inequality, sufficient conditions are obtained in terms of linear matrix inequalities to guarantee the mean‐square exponential stability of the considered system. Eventually, a numerical example is provided to demonstrate the effectiveness of the developed method.

Finite‐time H∞ bumpless transfer control for switched systems: A state‐dependent switching approach

“…Lyapunov asymptotic stability is an important topic, which involves stability and attractability. However, a blind pursuit of asymptotic stability on switched systems may generate undesired transient behavior and lead to mechanical damage or fatigue loading in practice …”

“…However, a blind pursuit of asymptotic stability on switched systems may generate undesired transient behavior and lead to mechanical damage or fatigue loading in practice. [5][6][7] In order to describe the transient behavior of system state, a concept of finite-time stability is introduced by Dorato, 8 which restricts the state to remain within a prescribed bound over a fixed-time interval. 9,10 Finite-time stability differs with Lyapunov asymptotic stability since the former focus upon the quantitative behavior of a dynamical system over a finite-time interval while the latter is more concerned with the qualitative properties over an infinite interval.…”

Probability Based Stochastic Iterative Learning Control for Batch Processes With Actuator Faults

“…A great deal of achievements has been proposed, such as the reliable control, adaptive control and control with stochastic faults on 1D system, which is only related to time direction [27]- [36]. However, the fruits in fault-tolerant predictive control and reliable guaranteed cost control based on 2D system are few [37]- [44]. For batch processes with linear uncertainty, time delay, and multi-phase, a large number of results have emerged in the study of fault-tolerant control [45]- [50].…”

A New Switched State Jump Observer for Traffic Density Estimation in Expressways Based on Hybrid-Dynamic-Traffic-Network-Model

“…In addition, for other system models, corresponding observer design methods were also studied [19,20,21]. In reference [22], based on a hybrid 2-D model of the switched stochastic systems, the observer was designed to solve the tracking control problem. The reduced-order state observers were studied in literature [23,24,25].…”