Adaptive Fuzzy Fast Finite-Time Tracking Control for Nonlinear Systems in Pure-Feedback Form with Unknown Disturbance

Ming Chen,Huanqing Wang,Ke Xu,Xiaoping Liu

doi:10.1155/2020/6347913

Abstract

In this paper, based on the fast finite-time stability theorem, an adaptive fuzzy control problem is considered for a class of nonlinear systems in pure-feedback form with unknown disturbance. In the controller design process, the mean value theorem is applied to address the nonaffine structure of the pure-feedback plant, the universal approximation capability of the fuzzy logic system (FLS) is utilized to compensate the unknown uncertainties, and the adaptive backstepping technique is used to design the controller model. Combined with the selection of the appropriate Lyapunov function at each step, a fuzzy-based adaptive tracking control scheme is proposed, which ensures that all signals in the closed-loop system are bounded and tracking error converges to a small neighborhood of the origin in fast finite-time. Finally, simulation results illustrate the validity of the proposed approach.

Highlights

During the recent years, the topics related to the field of nonlinear control have attracted a lot of attention [1,2,3]
The adaptive control combined with the backstepping technique has provided a systematic framework model-based for control design. e adaptive backstepping control method solves the control design problem for nonlinear systems with unmatched conditions and uncertain parameters and ensures the stability of the closed-loop system successfully
The mean value theorem is applied to deal with the nonaffine problem of the pure-feedback systems, fuzzy logic system (FLS) are adopted to approximate packaged unknown nonlinearities, and an improved adaptive fuzzy fast finitetime controller is designed via the backstepping technique. e stability of the closed-loop systems is guaranteed in fast finite-time

Summary

Introduction

The topics related to the field of nonlinear control have attracted a lot of attention [1,2,3]. It is a difficult but meaningful unsolved issue to develop an adaptive fuzzy fast finite-time tracking control scheme for nonlinear systems in pure-feedback form It is the main motivation of this paper. The mean value theorem is applied to deal with the nonaffine problem of the pure-feedback systems, FLSs are adopted to approximate packaged unknown nonlinearities, and an improved adaptive fuzzy fast finitetime controller is designed via the backstepping technique. (2) Combined the traditional adaptive backstepping technique with the characteristics of the radial basis function of fuzzy logic systems, by applying the mean value theorem and the fast finite-time theory, the system structure is simplified so that reduces complexity of the controller design.

Problem Formulation and Preliminaries

Adaptive Fuzzy Controller Design