Adaptive Stabilization Control for a Class of Complex Nonlinear Systems Based on T-S Fuzzy Bilinear Model

Jinsheng Xing,Naizheng Shi

doi:10.1155/2015/659521

Abstract

This paper proposes a stable adaptive fuzzy control scheme for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is established to represent the unknown complex systems. A parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error due to fuzzy modelling and the sufficient conditions of the closed-loop system stability with respect to decay rateαare derived by linear matrix inequalities (LMIs). Then the errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. The main contribution is to deal with the differences between the T-S fuzzy bilinear model and the real system; a global asymptotically stable adaptive control scheme is presented for real complex systems. Finally, illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

Highlights

Takagi-Sugeno (T-S) model-based fuzzy control is an effective and flexible tool for control of nonlinear systems
The errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved
This paper proposes a new modelling method based on the multiple inputs T-S fuzzy bilinear model which is used to approximate nonlinear system; the parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error caused by fuzzy modelling

Summary

Introduction

Takagi-Sugeno (T-S) model-based fuzzy control is an effective and flexible tool for control of nonlinear systems. A novel direct T-S fuzzy neural online modelling and control method for a class of nonlinear systems with parametric uncertainties has been proposed, which utilized T-S fuzzy neural model to approximate the virtual linear system and designed the online identification algorithm and robust adaptive tracking controller in [10, 11], respectively. Considering the differences of the fuzzy model and the reality systems, in the paper, a stable adaptive fuzzy control for complex nonlinear systems is presented based on multiple inputs T-S fuzzy bilinear system with parameters uncertainties. The contributions of this paper are as follows: (i) the differences between T-S fuzzy bilinear model and the real system are considered in the modelling and analysis; (ii) a global asymptotical stable adaptive control scheme is presented for real systems; (iii) a sufficient condition of the closed-loop systems is given. Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded

Problem Statement and Basic Assumptions

Control Design and Stability Analysis

Simulations

Conclusion