Fuzzy Adaptive Prescribed Performance Tracking Control for Uncertain Nonlinear Systems With Unknown Control Gain Signs

Wei Xiang,Heng Liu

doi:10.1109/access.2019.2946601

Abstract

This work addresses fuzzy adaptive tracking control of uncertain nonlinear systems with unknown control gain signs. Nussbaum functions are used to eliminate the effect of unknown control directions (i.e. unknown control gain signs). In order to make tracking errors approach a predefined neighborhood, two controllers are developed by the aid of fuzzy adaptive prescribed performance control (PPC) technique. The controlled system is transformed to an equivalent one by using appropriate transformation function. Under the proposed tracking controllers without accurate initial errors, the boundedness of all involved variables is guaranteed. Moreover, the tracking errors can remain within the small prescribed performance bounds (PPBs). Finally, simulation results show the effectiveness of the proposed methods.

Highlights

Many scholars have investigated the stability problem for MIMO nonlinear systems because most practical systems are multiple variables and exhibit nonlinear uncertain dynamic behavior
Combining with Nussbaum function, Boulkroune et al [12] proposed a fuzzy adaptive controller to deal with the problem of the unknown sign of the control gain matrix for MIMO nonlinear systems
The tracking error ei = xi − xdi is limited within prescribed performance constraint (see (7)), where xdi is the reference signal

Summary

INTRODUCTION

Many scholars have investigated the stability problem for MIMO nonlinear systems because most practical systems are multiple variables and exhibit nonlinear uncertain dynamic behavior. Bu et al [25] proposed back-stepping controllers based on a new performance function and achieved the convergence of tracking errors with small overshoot. The transformation function, another factor in controller design, needs to be reasonably constructed. Inspired by the above works, the main advantages of this paper are highlighted as follows: (1) The proposed control schemes can avoid the singular problem, which arises from the fuzzy estimation of control gains gi(x); (2) Even if initial values can not be given accurately and the PPB is very small, the proposed control schemes can overcome these two problem.

PRELIMINARIES

SIMULATION STUDIES

CONCLUSION