A novel control system for synchronizing chaotic systems in the presence of communication channel time delay; case study of Genesio-Tesi and Coullet systems

Abstract

Time delay is one of the challenges that may occur in the communication channels. The control of chaotic systems due to time delay is a challenging purpose. This paper defines a synchronization system where the Genesio-Tesi is the master, and the Coullet is the slave system. A suitable observer-based sliding mode controller is designed for the goal of synchronization with the communication channel’s time delay. The proposed control system consists of state and disturbance observers and a controller. The state, disturbance observers, and controller are designed to synchronize the chaotic systems. The state observer estimates the master system states, the disturbance observer estimates the model of the uncertainties and external disturbances, and the controller uses the information from the state and disturbance observers in real time. These state and disturbance observers and controller work simultaneously. The proposed controller is based on the Sliding Mode Control (SMC) method and fixed-time stability concepts. This control system is compared with finite-time and asymptotical control systems by defining three performance criteria IAE, ITAE, and ISV. The proposed control method is robust against uncertainties and external disturbances and chattering-free. The MATLAB/Simulink software simulates the control systems and compares their results.