Adaptive Asymptotic Regulation for Uncertain Nonlinear Stochastic Systems with Time-Varying Delays

Xuemiao Chen,Jing Li,Qianjin Zhao,Ziwen Wu

doi:10.3390/sym13122284

Abstract

In this paper, for a class of uncertain stochastic nonlinear systems with input time-varying delays, an adaptive neural dynamic surface control (DSC) method is proposed. To approximate the unknown continuous functions online, the neural network approximation technique was applied, and based on the DSC scheme, the desired controller was constructed. A compensation system is presented to compensate for the effect of the input delay. The Lyapunov–Krasovskii functionals (LKFs) were employed to compensate for the effect of the state delay. Compared with the existing works, based on using the DSC scheme with the nonlinear filter and stochastic Barbalat’s lemma, the asymptotic regulation performance of this closed-loop system can be guaranteed under the developed controller. To certify the availability for the designed control method, some simulation results are presented.

Highlights

In recent decades, due to the wide existence of random disturbances in real engineering applications, a large amount of achievements, with respect to the adaptive control problem for stochastic systems, have been reported [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
The literature [34,35,36,37,38,39,40,41,42,43,44] just focuses on the systems with state time-invariant delays and time-vary delays and, for a class of uncertain stochastic nonlinear system with state and input time varying delays, an adaptive neural dynamic surface control (DSC) scheme will be established in this paper, The main contributions of this paper are as follows: (i) This paper addresses the adaptive neural DSC problem for a class of uncertain stochastic nonlinear systems with state and input time-varying delays, firstly
This paper considers the following stochastic nonlinear system

Summary

Introduction

Due to the wide existence of random disturbances in real engineering applications, a large amount of achievements, with respect to the adaptive control problem for stochastic systems, have been reported [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. The adaptive control problems of stochastic nonlinear systems are addressed in [1,2,3,4] by using the output–feedback control method. For uncertain high-order stochastic nonlinear systems, the adaptive control problems are studied in [5,6,7], and the system stability can be ensured under the desired state feedback controller. The adaptive neural tracking problem for the uncertain stochastic nonlinear systems is presented in [12,13] where the unknown hysteresis is presented. For a class of stochastic interconnected non-strict feedback systems with dead zones, an adaptive neural DSC method is proposed in [15], and the “explosion of complexity” is avoided

Objectives

Results

Conclusion