Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems.

Yang Li,Jianhua Zhang,Xiaoyun Ye,Cheng Siong Chin

doi:10.3390/e23080963

Abstract

This paper examines the adaptive control of high-order nonlinear systems with strict-feedback form. An adaptive fixed-time control scheme is designed for nonlinear systems with unknown uncertainties. In the design process of a backstepping controller, the Lyapunov function, an effective controller, and adaptive law are constructed. Combined with the fixed-time Lyapunov stability criterion, it is proved that the proposed control scheme can ensure the stability of the error system in finite time, and the convergence time is independent of the initial condition. Finally, simulation results verify the effectiveness of the proposed control strategy.

Highlights

The adaptive trajectory tracking control of uncertain nonlinear systems has made a significant breakthrough [1,2,3]
This article consists of the following sections: in Section 2, a strict-feedback high-order nonlinear mathematical description of the problem is presented; in Section 3, the adaptive fixed-time neural network control scheme for the strict-feedback high-order nonlinear system is designed; in Section 4, simulation results show the effectiveness of the proposed control strategy; in Section 5, the conclusion of the article is presented
The main contributions of this paper are as follows: the fixed-time control problem of strict-feedback high-order nonlinear systems is solved; the Lyapunov function is designed for each subsystem; at the same time, combined with adaptive backstepping technology, an adaptive neural network fixed-time controller is designed

Summary

Introduction

The adaptive trajectory tracking control of uncertain nonlinear systems has made a significant breakthrough [1,2,3]. The ideal weights of NNs are unknown, and it is difficult to obtain a convergence time To solve this issue, fixed-time neural network control is an appropriate selection of the control method. The fixed-time neural network adaptive controller is present for nonlinear high-order systems. The combination of the neural network adaptive control with fixed-time Lyapunov stability theory for high-order nonlinear system control problems. This article consists of the following sections: in Section 2, a strict-feedback high-order nonlinear mathematical description of the problem is presented; in Section 3, the adaptive fixed-time neural network control scheme for the strict-feedback high-order nonlinear system is designed; in Section 4, simulation results show the effectiveness of the proposed control strategy; in Section 5, the conclusion of the article is presented

Problem Formation and Preliminaries

Main Results

Numerical Examples

Conclusions