Robust Adaptive Control for a Class of T-S Fuzzy Nonlinear Systems with Discontinuous Multiple Uncertainties and Abruptly Changing Actuator Faults

Xin Ning,Zheng Wang,Yao Zhang,Paolo Bellavista

doi:10.1155/2020/8863073

Abstract

In the complex environment, the suddenly changing structural parameters and abrupt actuator failures are often encountered, and the negligence or unproper handling method may induce undesired or unacceptable results. In this paper, taking the suddenly changing structural parameters and abrupt actuator failures into consideration, we focus on the robust adaptive control design for a class of heterogeneous Takagi–Sugeno (T-S) fuzzy nonlinear systems subjected to discontinuous multiple uncertainties. The key point is that the switch modes not only vary with the system time but also vary with the system states, and the intrinsic heterogeneous characteristics make it difficult to design stable controllers. Firstly, the concepts of differential inclusion are introduced to describe the heterogeneous fuzzy systems. Meanwhile, a fundamental lemma is provided to demonstrate the criteria of the boundness for a Filippov solution. Then, by using the set-valued Lie derivative of the Lyapunov function and introducing a vector of specific continuous functions, the closed-loop T-S fuzzy differential inclusion systems are proved to be ultimately bounded. The sufficient conditions for system stability are derived in term of linear matrix inequalities (LMIs), which can be solved directly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control algorithm.

Highlights

As it is well-known, the T-S fuzzy model is a powerful tool for the analysis and control design of nonlinear systems [1,2,3,4]. erefore, a great wealthy of results has been achieved for T-S fuzzy systems in the past decades
In [5], the parameterized linear matrix inequality technique has been investigated for T-S fuzzy control systems
In [6], by using the linear matrix inequalities (LMIs) and sum-of-squares-based approach, an output regulator has been constructed for the polynomial fuzzy control systems

Summary

Introduction

As it is well-known, the T-S fuzzy model is a powerful tool for the analysis and control design of nonlinear systems [1,2,3,4]. erefore, a great wealthy of results has been achieved for T-S fuzzy systems in the past decades. Chang et al [18] focused on the robust adaptive control design for a class of heterogeneous T-S fuzzy nonlinear systems subjected to discontinuous multiple uncertainties. In [36], an adaptive fuzzy tracking control problem has been investigated for a class of nonstrict-feedback systems with unmeasured states and unknown nonlinearities. Motivated by the above considerations, this paper is committed to develop an effective control structure for the T-S fuzzy heterogeneous systems with discontinuous multiple uncertainties and abruptly changing actuator faults. (i) To the best of the authors’ knowledge, it is the first control solution for the T-S fuzzy systems subjected to heterogeneous uncertainties and system structures, which keep switching with both the system time and the system states. (iii) By proposing a specific vector of continuous functions, the closed-loop multivariable T-S fuzzy differential inclusion systems are proved to be bounded for the first time

Problem Formulation and Preliminaries

Main Results

Simulation Study

Conclusions