Transmission Projective Synchronization of Multiple Non-Identical Coupled Chaotic Systems Using Sliding Mode Control

Abstract

This paper presents the control design method for the transmission projective synchronization (TPS) of the Multiple Non-identical Coupled Chaotic systems using sliding mode. A total of four different cases of chaotic systems are studied which are: 1) systems with known parameters without fault; 2) systems with known parameters with a fault; 3) systems with unknown parameters without fault; and 4) systems with unknown parameters and fault occurrence. In first and third cases, the controllers are designed using sliding mode, and adaptive integral sliding mode (AISM) is used to design controllers for the second and fourth cases. To employ AISM, the error dynamics is broken into a structure comprising a nominal and some unknown part, which are adaptively computed. The error dynamics are stabilized by AISM control which consists of a nominal and a compensator control. To avoid the chattering phenomenon, smooth continuous compensator control is used instead of the traditional discontinuous control. The stability of adaptive law and compensator is derived using a Lyapunov function which becomes strictly negative. Finally, the simulations of a numerical example verify the TPS behavior.

Keywords

• Multiple coupled chaotic system
• transmission projective synchronization
• adaptive integral sliding mode control
• Lyapunov function