Adaptive synchronization of single-degree-of-freedom oscillators with unknown parameters

Adaptive synchronization of single-degree-of-freedom oscillators with unknown parameters

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Article ID: iaor20121894
Volume: 218
Issue: 12
Start Page Number: 6833
End Page Number: 6840
Publication Date: Feb 2012
Journal: Applied Mathematics and Computation
Authors: , ,
Keywords: optimization
Abstract:

In this paper, an adaptive control scheme is proposed for the synchronization of two single‐degree‐of‐freedom oscillators with unknown parameters. We only assume that the master system has the bounded solutions, which is generally satisfied for chaotic systems. Unlike the existing literature, the boundedness of the states of the slave system with control input is not necessarily known in advance. The boundedness of the controlled states is rigorously proved. The unknown parameters not only in the slave system but also in the master system are estimated by designing adaptive laws. By choosing appropriate Lyapunov function and employing Barbalat’s lemma, it is theoretically shown that the synchronization errors can converge to zero asymptotically. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed adaptive control design.

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