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Adaptive synchronization and parameter identification for Lorenz chaotic system with stochastic perturbations

Zhu Da-Wei Tu Li-Lan

Adaptive synchronization and parameter identification for Lorenz chaotic system with stochastic perturbations

Zhu Da-Wei, Tu Li-Lan
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  • Received Date:  21 September 2012
  • Accepted Date:  21 October 2012
  • Published Online:  05 March 2013

Adaptive synchronization and parameter identification for Lorenz chaotic system with stochastic perturbations

  • 1. Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 60904060, 61104127).

Abstract: In this paper, Lorenz chaotic system with stochastic perturbation and unknown parameters is investigated, in which the stochastic perturbations is one-dimensional random process of the standard Wiener. Based on stochastic Lyapunov stability theory, It formula and adaptive control method combined with three adaptive control laws and two adaptive control laws respectively, two mean square Asymptotic adaptive synchronization standards are put forward theoretically. These new standards are in a simple form and easy to deal with. Moreover, with these standards, not only drive system with stochastic perturbations can be synchronized with the respond system, but also unknown parameters in the system can be identified. Finally, the Matlab numerical simulations confirm that the proposed results are correct and effective.

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