Adaptive synchronization control of chaotic nonlinear systems in the presence of input saturation and actuator faults

In this paper, the control problem is investigated for Jerk chaotic systems against unknown parameters, actuator faults and input saturation. The considered actuator fault covers both of the stuck faults and loss of effectiveness faults in actuators. The values, times and patterns of the considered faults are completely unknown. That is, during the system operation it is unknown when, by how much and which actuators fail. A robust adaptive controller is presented based on the backstepping design method to achieve complete synchronization of the identical Jerk chaotic systems. By introducing the new Lyapunov functions, it is proved that all the closed loop signals are bounded and the tracking error converges to a small neighborhood of the origin. The proposed adaptive method compensates the actuator faults without any need for explicit fault detection. Simulation results represent that the designed controller can synchronize the identical chaotic systems in the presence of actuator fault, input saturation and unknown parameters.