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A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances. (English) Zbl 1238.93026
Summary: A Robust Adaptive Sliding Mode Controller (RASMC) is introduced to synchronize two different chaotic systems in the presence of unknown bounded uncertainties and external disturbances. The structure of the master and slave chaotic systems has no restrictive assumption. Appropriate adaptation laws are derived to tackle the uncertainties and external disturbances. Based on the adaptation laws and Lyapunov’s stability theory, an adaptive sliding control law is designed to ensure the occurrence of the sliding motion even when both master and slave systems are perturbed with unknown uncertainties and external disturbances. Since the conventional sliding mode controllers contain the sign function, the undesirable chattering is occurred. We propose a new simple adaptive scheme to eliminate the chattering. Finally, numerical simulations are presented to verify the usefulness and applicability of the proposed control strategy.

MSC:
93B12 Variable structure systems
34H10 Chaos control for problems involving ordinary differential equations
93B35 Sensitivity (robustness)
93C40 Adaptive control/observation systems
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