Synchronization of a Non-Equilibrium Four-Dimensional Chaotic System Using a Disturbance-Observer-Based Adaptive Terminal Sliding Mode Control Method.

Shaojie Wang,Jesus M Munoz-Pacheco,Hadi Jahanshahi,Raúl Alcaraz,Amin Yousefpour,Abdullahi Yusuf,Shaobo He

doi:10.3390/e22030271

Abstract

In this paper, dynamical behavior and synchronization of a non-equilibrium four-dimensional chaotic system are studied. The system only includes one constant term and has hidden attractors. Some dynamical features of the governing system, such as invariance and symmetry, the existence of attractors and dissipativity, chaotic flow with a plane of equilibria, and offset boosting of the chaotic attractor, are stated and discussed and a new disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method with input saturation is proposed for the control and synchronization of the chaotic system. To deal with unexpected noises, an extended Kalman filter (EKF) is implemented along with the designed controller. Through the concept of Lyapunov stability, the proposed control technique guarantees the finite time convergence of the uncertain system in the presence of disturbances and control input limits. Furthermore, to decrease the chattering phenomena, a genetic algorithm is used to optimize the controller parameters. Finally, numerical simulations are presented to demonstrate the performance of the designed control scheme in the presence of noise, disturbances, and control input saturation.

Highlights

Chaotic systems are currently attracting a considerable amount of attention thanks to their potential applications in a variety of fields [1,2,3,4,5,6]
Since Rössler studied the first four-dimensional chaotic system [21], a four-dimensional continuous-time autonomous no equilibria system with a cubic nonlinear term was proposed by Pham et al [22]
A memristive system without any equilibrium was presented by Bao et al [23], who demonstrated that this system was able to exhibit chaotic, hyperchaotic, transient hyperchaotic, as well as periodic dynamics

Summary

Introduction

Chaotic systems are currently attracting a considerable amount of attention thanks to their potential applications in a variety of fields [1,2,3,4,5,6]. Different chaotic systems have been introduced, Entropy 2020, 22, 271; doi:10.3390/e22030271 www.mdpi.com/journal/entropy. Some research studies have proposed four-dimensional chaotic systems with special features. Since Rössler studied the first four-dimensional chaotic system [21], a four-dimensional continuous-time autonomous no equilibria system with a cubic nonlinear term was proposed by Pham et al [22]. A memristive system without any equilibrium was presented by Bao et al [23], who demonstrated that this system was able to exhibit chaotic, hyperchaotic, transient hyperchaotic, as well as periodic dynamics. A four-dimensional chaotic system including nine terms and only one constant term, which either has a line of equilibria or does not possess equilibria, was very recently proposed by Zhang et al [24]

Methods

Results

Conclusion