Forced Sliding Mode Control for Chaotic Systems Synchronization

Abstract

Synchronization of chaotic systems is considered to be a common engineering problem. However, the proposed laws of synchronization control do not always provide robustness towards the parametric perturbations. The purpose of this article is to show the use of synergy-cybernetic approach for the construction of robust law for Arneodo chaotic systems synchronization. As the main method of design of robust control, the method of design of control with forced sliding mode of the synergetic control theory is considered. To illustrate the effectiveness of the proposed law it's compared in this article with the classical sliding mode control. The distinctive features of suggested robust control law are the more good compensation of parametric perturbations (better performance indexes --- the root-mean-square error, average absolute value of error) without designing perturbation observers, the ability to exclude the chattering effect, less energy-consuming and a simpler analysis of the stability of a closed-loop system. Offered approach will allow a new consideration for the design of robust control laws for chaotic systems, taking into account the ideas of directed self-organization and robust control. It can be used for synchronization other chaotic systems.Mathematics Subject Classification (2020) 93B35 · 93B52 · 93C30 · 93D21 · 34H10

Realizing stochastic fixed-time synchronization between two nonlinear chaotic finance systems

“…In other words, the chaotic behavior is unpredictable and often undesirable, which could result in instability of a single system and desynchronization for two or more systems. In order to stabilize or synchronize one or more chaotic systems, past years have witnessed novel control techniques, such as the bang-bang control [7], sliding mode control(SMC) [8], active control [9], impulsive control [10], and so forth.…”