Controlling and Synchronization of Chaotic System using FREN with Sliding Bounds

C. Treesatayapun and S. Uatrongjit



This article proposes a direct adaptive controller based on our adaptive network called Fuzzy Rules Emulated Network (FREN) and Sliding Mode Control (SMC). The SMC is applied to estimate the upper and lower bounds of the control signal to guarantee that the phase trajectories are directed towards the switching surface, and the proposed controller, FREN, generates a suitable control signal according to the given fuzzy control rules within these bounds. The structure of FREN resembles human knowledge in the form of fuzzy if-then rules. After selection of the initial value of network parameters, an online adaptive process based on Lyapunov’s criteria is performed to improve the controller’s performance. To demonstrate the system performances, the proposed FREN adaptive controller is applied to control and synchronize chaotic systems, that is, two-dimension and three-dimension Hénon maps respectively. The simulation results indicate that the proposed algorithm can satisfactorily control the trajectory of those chaotic systems, and comparisions with other chaotic control algorithms are given.

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