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Design of adaptive sliding mode controller for chaos synchronization with uncertainties. (English) Zbl 1060.93536

Summary: In this paper an adaptive sliding mode controller is presented for a class of master-slave chaotic synchronization systems with uncertainties. Using an adaptive technique to estimate the switching gain, an adaptive sliding mode controller is then proposed to ensure that the sliding condition is maintained in finite time. The proposed adaptive sliding mode control scheme can be implemented without the requirement that the bounds of the uncertainties and the disturbances should be known in advance. The concept of extended systems is used such that continuous control input is obtained using a sliding mode design scheme. By comparing with the results in the existed literatures, the results show that the master-slave chaotic systems with uncertainties can be synchronized accurately by this controller. Illustrative examples of chaos synchronization for uncertain Duffing-Holmes system are presented to demonstrate the superiority of the obtained results.

MSC:

93C10 Nonlinear systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
93C40 Adaptive control/observation systems
93B12 Variable structure systems
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