Adaptive Asymptotic Tracking Control for a Class of Uncertain Input-Delayed Systems with Periodic Time-Varying Disturbances

Xiaoman Yan,Jian Wu,Chunsheng Zhang,Dewen Cao,Defeng He

doi:10.1155/2021/6646716

Abstract

In this paper, the problem of adaptive asymptotic tracking control for a class of uncertain systems with periodic time-varying disturbances and input delay is studied. By combining Fourier series expansion (FSE) with radial basis function neural network (RBFNN), a hybrid function approximator is used to learn the functions with periodic time-varying disturbances. At the same time, the dynamic surface control technique with a nonlinear filter is used to avoid the “complexity explosion” problem in the process of traditional backstepping technology. Ultimately, all closed-loop signals are guaranteed to be semiglobally uniformly bounded, and the given reference signal can be asymptotically tracked by the output signals of system. A simulation example is given to verify the effectiveness of the proposed control scheme.

Highlights

With the deepening of the research on uncertain nonlinear control systems, more and more scholars have carried out indepth research on this problem and achieved remarkable results. e uncertainties appear in nonlinear systems in strict-feedback form [1,2,3,4,5,6], purefeedback form [7, 8], multiple-input-multiple-output (MIMO) form [9,10,11], time-delay form [12, 13], switched form [14,15,16,17,18,19], and discrete-time form [20, 21]
For a class of uncertain MIMO nonlinear systems with given tracking performance, the error-driven nonlinear feedback design method [10] is proposed to improve the dynamic performance of fuzzy adaptive moving surface control. e dynamic output feedback fault-tolerant controller [12] is designed to solve the problems of fault estimation and fault-tolerant controller design for a class of discrete-time fuzzy systems. e adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems [14] is studied
For a class of single input single output strict-feedback fractional-order uncertain nonlinear systems, the dynamic surface control method based on fractional-order filter [32] is proposed to avoid the inherent “complexity explosion” problem in the backstepping design process. e problem of adaptive fuzzy dynamic surface control [33] is studied for a class of nonstrict feedback nonlinear systems with unknown virtual control coefficients and full state constraints. e dynamic surface control technology [34] is used to solve the “complexity explosion” problem and combines the Nussbaum function to solve the problem of unknown control direction

Summary

Introduction

With the deepening of the research on uncertain nonlinear control systems, more and more scholars have carried out indepth research on this problem and achieved remarkable results. e uncertainties appear in nonlinear systems in strict-feedback form [1,2,3,4,5,6], purefeedback form [7, 8], multiple-input-multiple-output (MIMO) form [9,10,11], time-delay form [12, 13], switched form [14,15,16,17,18,19], and discrete-time form [20, 21]. For a class of single input single output strict-feedback fractional-order uncertain nonlinear systems, the dynamic surface control method based on fractional-order filter [32] is proposed to avoid the inherent “complexity explosion” problem in the backstepping design process. E main work is as follows: (1) in this paper, the problem of adaptive asymptotic tracking control for a class of nonlinear uncertain systems with periodic timevarying disturbances and input delay is studied. To solve this problem, we propose a new adaptive control scheme. A simulation example is given to verify the effectiveness of the proposed control scheme

Problem Description and Preliminaries

Simulation Example

Conclusions