Chaos synchronization of multi time-delayed chaotic Rossler system with uncertainties and external disturbances via sliding adaptive fuzzy controller

In this study, a sliding adaptive fuzzy controller is applied for chaos synchronization of two multi time-delayed Rossler systems. Two fuzzy systems with adaptation laws obtained from gradient descent method with novel cost function are employed to achieve two control laws. In this method, the first derivation of the Lyapunov function is considered as the cost function which must be minimized. To design the controller, two sliding surfaces are defined as the inputs of fuzzy systems. Lyapunov stability theory is used to guarantee the stability of error dynamics. The sliding adaptive fuzzy control scheme can be implemented without the requirement that the bounds of the uncertainties and the disturbances. It should be note that the control procedure is done with only two control signals. Simulation results of chaos synchronization for uncertain Rossler system are presented to demonstrate the validity and effectiveness of the proposed method for synchronization of two identical multi time-delayed chaotic systems.