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Stochastic fixed-time synchronization of chaotic systems via smooth control

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Abstract

This paper is concerned with the fixed-time synchronization of two chaotic systems, and further takes the stochastic noise into consideration. A novel smooth control protocol is developed to overcome the chattering problem caused by the signum function contained in the conventional finite/fixed-time controllers. In the light of the (stochastic) fixed-time stability theory, the sufficient conditions are derived for achieving the (stochastic) fixed-time synchronization of two chaotic systems, in which the upper bound of synchronization time can be estimated in advance. Finally, two classical chaotic systems are used to verify the validity of proposed theoretical results, which shows that fixed-time synchronization of chaotic systems is robust to noise perturbation.

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Acknowledgments

This work was supported by the Fundamental Research Funds for the Central Universities [No. JUSRP121069], National Natural Science Foundation of China [No. 61972182, No. 61672264], the National Key R&D Program of China [No. 2016YFB0800305], and the Fundamental Research Funds of Suzhou University of Science and Technology [No. 332114604].

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Authors and Affiliations

  1. School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, China

    Jie Wu & Xiaofeng Wang

  2. School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou, China

    Ru-ru Ma

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  1. Jie Wu
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  2. Xiaofeng Wang
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Correspondence to Jie Wu.

Additional information

Jie Wu is currently a Lecturer at the School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, China. He received his B.S. degree from Hainan Normal University in 2013, his M.S. degree from China University of Mining and Technology in 2015, and his Ph.D. in Electronic Engineering from Fudan University, Shanghai, China in 2020. His research interests include stability of chaotic systems, PMSM, and synchronization of complex networks with applications.

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Wu, J., Wang, X. & Ma, Rr. Stochastic fixed-time synchronization of chaotic systems via smooth control. J Mech Sci Technol 35, 4161–4168 (2021). https://doi.org/10.1007/s12206-021-0828-1

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  • DOI: https://doi.org/10.1007/s12206-021-0828-1

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