Adaptive fixed-time anti-synchronization and synchronization control for Liu-Chen-Liu chaotic systems with actuator faults

In this paper, the fixed-time anti-synchronization and synchronization fault-tolerant control problem is considered for two identical Liu-Chen-Liu chaotic systems with uncertain parameters. With the help of fixed-time stability theory and adaptive backstepping method, we propose two novel adaptive controllers. In the control scheme proposed in this paper, the adaptive backstepping technique is used to deal with the unknown parameters contained in the chaotic systems. Besides, the piecewise functional method is used to solve the singularity problem in the controller design process. The designed controllers achieve anti-synchronization and synchronization of two identical Liu-Chen-Liu chaotic systems within the preset time interval. Simulation results are conducted to show the effectiveness of two proposed adaptive controllers.