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An improved approaching law based on sliding mode controller for Duffing-Holmes systems with uncertainties

In this paper a sliding mode controller is presented for a class of master-slave chaotic systems with uncertainties. In order to avoid the effects of uncertainties, an improved approaching law based on time-variable parameters is then proposed. In the approaching law, parameters are not constants, but they are time-variable according to the given variable laws. The proposed scheme can be implemented on the condition that the bounds of the uncertainties and the disturbances should be known in advance. At the same time, we need not know the idiographic expressions of the uncertainties and the disturbances. After using the above method, chaos synchronization can still be realized even though the slave system is uncertain. At last, an illustrative example of chaos synchronization for uncertain Duffing-Holmes system is presented to demonstrate the performance of the proposed method.