An Integral Sliding Mode Control of Uncertain Chaotic Systems via Disturbance Observer

Hua Zhang

doi:10.1155/2021/6628116

Abstract

This paper proposes an integral sliding mode control (ISMC) method of a class of uncertain chaotic systems with saturation inputs. Firstly, fuzzy logic system (FLS) is used to estimate the unknown nonlinear function. Then, a disturbance observer is constructed to estimate a compound disturbance, which contains the external disturbance, the error of saturation input and control output, and the fuzzy estimation error. Subsequently, a proposed integral sliding mode controller can ensure that all signals of the closed-loop system are ultimately bounded, and based on the dynamic system of the integral sliding mode variable itself, the ultimate bound of the tracking error can be estimated. Simulation results show that the proposed ISMC method is more effective than the traditional ISMC method.

Highlights

Due to the unpredictability and the sensitivity to initial conditions, the chaotic system makes itself useful in many fields such as information processing, secure communications, and mechanical systems [1, 2]
Wang et al [11] proposed a nonsingular terminal SMC method to ensure that all states of the chaotic system reach the designed sliding surface in finite time
Inspired by the abovementioned works, this paper investigates the problem of integral sliding mode control for a class of uncertain chaotic systems with saturation inputs, and the proposed integral SMC method can guarantee all signals of the closed-loop system are bounded and accurately estimate system uncertainties. e main contributions of this paper are summarized as follows: (1) Compared with the traditional integral sliding mode variable, the integrated sliding mode variable proposed in this paper can estimate the error bound by its own dynamics when the boundedness of the integrated sliding mode variable is guaranteed

Summary

Introduction

Due to the unpredictability and the sensitivity to initial conditions, the chaotic system makes itself useful in many fields such as information processing, secure communications, and mechanical systems [1, 2]. Many methods have been proposed to stabilize or synchronize chaotic systems, such as adaptive control method [3, 4], backstepping control [5, 6], impulsive control [7], intermittent control [8], and sliding mode control [9,10,11,12,13,14]. Inspired by the abovementioned works, this paper investigates the problem of integral sliding mode control for a class of uncertain chaotic systems with saturation inputs, and the proposed integral SMC method can guarantee all signals of the closed-loop system are bounded and accurately estimate system uncertainties.

Preliminaries

Sliding Mode Control Design and Stability Analysis

Example

Conclusion