Non-Fragile Control for Variable Sampling Period Network Control System with Actuator Failure

Xin Tang

doi:10.11648/j.acis.20180604.11

Abstract

The guaranteed cost control problem is studied in this paper for a class of nonlinear discrete-time systems with both time-varying parametric uncertainty and actuator failures. At present, the researches on related fields of networked control systems are relatively mature, and many achievements have been made. But at the same time, most of the researches are focused on linear networked control systems, and the research on nonlinear networked control systems is relatively less. The goal is to design a non-fragile state feedback control law so that the closed-loop system is asymptotically stable and the closed-loop cost function value is no more than a specified upper bound for all admissible uncertainties. Firstly, the system model is established by using the method of variable sampling period. Secondly, the sufficient conditions for the asymptotic stability of the closed-loop system are given by using Lyapunov stability theory. Thirdly, based on the above researches, a non-fragile state feedback controller is designed by using linear matrix inequality (LMI). In the end, through the study of this paper, the cost function of the system under the designed non-fragile guaranteed cost controller does not exceed the given upper bound. This paper considers the actuator failure, and gives the design method of the non-fragile guaranteed cost controller of the nonlinear network control system, and makes a contribution to the field of network control system.

Highlights

In the modern society, the Internet is widely used in various fields
Theorem 1: For the closed-loop system (7) and the cost function (8), the following matrix inequalities holds if there exists a matrix K, ∆K, R > 0 and a scalar Γ > 0
Actuator failure is the main cause of system control performance failure

Summary

Introduction

The Internet is widely used in various fields. Many high-tech fields and large enterprises, such as resource sharing, automated factories, robots manufactures, advanced aerospace undertakings and electrified transport vehicle manufacturres, depend heavily on the networks. Xin Tang et al.: Non-Fragile Control for Variable Sampling Period Network Control System with Actuator Failure performance control, and controller design problems of related systems. Sufficient conditions for the existence of non-fragile guaranteed cost controllers for nonlinear systems with additive and multiplicative disturbances were given in the form of linear matrix inequalities [20]. Aiming at the control input constraints and controller gain disturbances, Gao Xingquan proposed a non-fragile guaranteed cost state feedback control method for a class of norm-bounded parameter uncertain linear systems, and derived a new sufficient condition for solving the constrained non-fragile guaranteed cost control law [21]. Yu Shuiqing studied the non-fragile guaranteed cost control problem for a class of nonlinear networked control systems with stochastic delay and controller gain disturbances [22]. This paper, designs a non-fragile controller for a class of nonlinear networked control systems with variable sampling period. Symbol description: The symbol * indicates the block matrix in a symmetric matrix, A is the transpose matrix of A

Problem Description

Stability Analysis

G Kα 00 00

Conclusion