Observer-Based Robust Adaptive Fuzzy Control for MIMO Nonlinear Uncertain Systems with Delayed Output

Chiang Cheng Chiang

doi:10.1155/2013/215201

Abstract

An observer-based robust adaptive fuzzy control scheme is presented to tackle the problem of the robust stability and the tracking control for a class of multiinput multioutput (MIMO) nonlinear uncertain systems with delayed output. Because the nonlinear system functions and the uncertainties of the controlled system including structural uncertainties are supposed to be unknown, fuzzy logic systems are utilized to approximate these nonlinear system functions and the upper bounded functions of the uncertainties. Moreover, the upper bound of uncertainties caused by these fuzzy modeling errors is also estimated. In addition, the state observer based on state variable filters is designed to estimate all states which are not available for measurement in the controlled system. By constructing an appropriate Lyapunov function and using strictly positive-real (SPR) stability theorem, the proposed robust adaptive fuzzy controller not only guarantees the robust stability of a class of multivariable nonlinear uncertain systems with delayed output but also maintains a good tracking performance. Finally, some simulation results are illustrated to verify the effectiveness of the proposed control approach.

Highlights

Controller design for nonlinear systems has been given a lot of attention in the control community during the last two decades
The study of robust stability of nonlinear uncertain systems in the presence of uncertainties is an important topic for the control design engineer
The main result of the proposed observer-based robust adaptive fuzzy control scheme is summarized in the following theorem

Summary

Introduction

Controller design for nonlinear systems has been given a lot of attention in the control community during the last two decades. The motivation of this paper is to synthesize an observer-based robust adaptive fuzzy control scheme to deal with the tracking control problem for a class of MIMO nonlinear uncertain systems with delayed output in the presence of uncertainties including the structural uncertainty. The robust control problem of MIMO nonlinear systems with delayed output in the presence of uncertainties will be considered in this paper. The problem of controller design for a class of MIMO nonlinear uncertain output-delay systems whose states are not available is considered.

Problem Formulation and Preliminaries

Observer-Based Robust Adaptive Fuzzy Controller Design and Stability Analysis

An Example and Simulation Results

Conclusion