Design of a nonlinear controller and its intelligent optimization for exponential synchronization of a new chaotic system

This paper deals with the synchronization problem of two chaotic systems in a master-slave configuration. The two systems are based on a new chaotic system recently reported by Akgul and Pehlivan in [1]. The global and exponential convergence to zero of the synchronization error is guaranteed by means of a nonlinear controller designed from the Lyapunov stability theory. In order to find the appropriate parameters of this controller, the compromise between magnitude of control signal and convergence speed is quantified by using a quadratic performance index. Next, such index is minimized via four different intelligent optimization algorithms: differential evolution, brain storm, cuckoo search, and harmony search. These four algorithms are exhaustively tested and the results are systematically compared. Finally, the performance of the optimized nonlinear controller is showed graphically.