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Function Approximation Technique Based Adaptive Control for Chaos Synchronization between Different Systems with Unknown Dynamics

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  • Control Theory and Applications
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Abstract

This paper presents a function approximation technique based immersion and invariance adaptive controller for chaos synchronization between nonidentical systems with unknown dynamics. In the proposed control scheme, the control system is reconstructed as the combination of a controllable linear system and a variation term from the original system. The variation term is treated as time-varying uncertainty and approximated by a group of weighted chosen basis functions. The immersion and invariance methodology is employed to design the adaptive control law such that both the synchronization error and uncertainty estimation error converge to zero. Two typical chaos synchronization problems are used in numerical simulations to verify the effectiveness and superiority of the proposed controller.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, IL, 61801, USA

    Yujie Wang

  2. Information Science and Engineering Department, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga, 525-8577, Japan

    Yang Bai & Mikhail Svinin

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  1. Yujie Wang
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  2. Yang Bai
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  3. Mikhail Svinin
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Correspondence to Yujie Wang.

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Yujie Wang received his B.S. degree from Nanjing University of Science and Technology in 2016. Currently, he is pursuing an M.S. degree at University of Illinois Urbana-Champaign. His research interests include robust control, adaptive control, and reinforcement learning.

Yang Bai received his B.S., M.S., and Ph.D. degrees in mechanical engineering from Kyushu University, Fukuoka, Japan, in 2014, 2016, and 2019, respectively. He has been an assistant professor at the College of Information Science and Engineering, Ritsumeikan University, since 2019. Dr. Bai is a member of the Institute of Electrical and Electronic Engineers (IEEE) and the Robotics Society of Japan (RSJ). His current research interests include robust adaptive control and multi-agent control.

Mikhail Svinin received his Ph.D. degree from St. Petersburg Informatics and Automation Institute, St. Petersburg, Russia, and conducted postdoctoral studies at the Institute of Automatic Control, Darmstadt Technical University, Germany, as an Alexander von Humboldt Research Fellow, and at Tohoku University, Japan, as a JSPS post-doctoral fellow. Before joining the College of Information Science and Engineering, Ritsumeikan University, he was with the Department of Mechanical Engineering, Kyushu University. His research interests include robotics, control theory, and analytical mechanics. Dr. Svinin is a member of the Institute of Electrical and Electronic Engineers (IEEE) and the Robotics Society of Japan (RSJ). He received best paper awards at the IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2008, and the JSME International Conference on Advanced Mechatronics, 2004.

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Wang, Y., Bai, Y. & Svinin, M. Function Approximation Technique Based Adaptive Control for Chaos Synchronization between Different Systems with Unknown Dynamics. Int. J. Control Autom. Syst. 19, 2611–2621 (2021). https://doi.org/10.1007/s12555-020-0412-y

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