In this paper, an adaptive control scheme is offered to synchronize two different uncertain chaotic systems. It is assumed that the whole dynamics of both master and slave chaotic systems and their bounds are unknown and different. The error system stabilization is achieved in two cases: with input nonlinearities and without input nonlinearities. We design an adaptive control scheme based on the state boundedness property of the chaotic systems. The proposed method does not need any information about nonlinear/linear terms of the chaotic systems. It only uses an adaptive feedback control strategy. The stability of the proposed controllers is proved by using the Lyapunov stability theory. Finally, the designed adaptive controllers are applied to synchronize two different pairs of the chaotic systems (Lorenz–Chen and electromechanical device–electrostatic transducer).
Synchronization of Unknown Uncertain Chaotic Systems Via Adaptive Control Method
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 20, 2014; final manuscript received July 3, 2014; published online April 2, 2015. Assoc. Editor: Stefano Lenci.
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Aghababa, M. P., and Hashtarkhani, B. (September 1, 2015). "Synchronization of Unknown Uncertain Chaotic Systems Via Adaptive Control Method." ASME. J. Comput. Nonlinear Dynam. September 2015; 10(5): 051004. https://doi.org/10.1115/1.4027976
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