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Boundary Output Feedback for Fixed-time Stabilization of Distributed Parameter Systems With Time and Space Dependent Reactivity

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  • Control Theory and Applications
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Abstract

The problem of boundary output feedback for fixed-time stabilization of parabolic distributed parameter systems with space and time dependent reactivity is considered by utilizing the backstepping method. An observer is constructed by applying the time-varying observer gain and boundary measurements, where the gain is unbounded as time approaches the terminal time. However, the fixed-time stability of error system is guaranteed by comparing the time growth rate of the observer gain with the decay rate of target error system state. Then, an observer-based output feedback boundary controller is established to achieve the fixed-time stabilization of the closed-loop system by combining the fixed-time stabilizing state feedback boundary controller and the fixed-time observer based on separation principle. Finally, a numerical simulation is shown to illustrate the effectiveness of the theoretical results.

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Author information

Authors and Affiliations

  1. College of Mathematics and Physics, Inner Mongolia Minzu University, Tongliao, 028000, China

    Chunxia Bao

  2. School of IoT Engineering, Jiangnan University, Wuxi, 214122, China

    Baotong Cui & Wei Wu

  3. School of Information Engineering, Binzhou University, Binzhou, 256600, China

    Bo Zhuang

Authors
  1. Chunxia Bao
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  2. Baotong Cui
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  3. Wei Wu
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  4. Bo Zhuang
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Corresponding author

Correspondence to Baotong Cui.

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This work is supported by China Postdoctoral Science Foundation (2018M642160) and Inner Mongolia Minzu University Doctoral Research Initiation Fund (BS680).

Chunxia Bao received her B.S. degree in mathematics and applied mathematics and an M.S. degree in operational research and cybernetics both from Inner Mongolia Normal University, Hohhot, China, in 2015 and 2018, respectively. She received her Ph.D. degree in control theory and control engineering from School of IoT Engineering in 2022, Jiangnan University, Wuxi, Jiangsu, China. Her research interests include boundary control of distributed parameter systems, fixed-time stabilization, and estimation of partial differential equations.

Baotong Cui received his Ph.D. degree in control theory and control engineering from the College of Automation Science and Engineering, South China University of Technology, in 2003. He was a postdoctoral fellow at Shanghai Jiaotong University from July 2003 to September 2005, and a visiting scholar at Department of Electrical and Computer Engineering, National University of Singapore from August 2007 to February 2008. He is now a professor in the School of IoT Engineering, Jiangnan University. His current research interests include control of distributed parameter systems, systems analysis, artificial neural networks, and chaos synchronization.

Wei Wu received his Ph.D. degree in electrical and information engineering from University of Kaiserslautern, Kaiserslautern, Germany. He is currently an Associate Professor with Jiangnan University, in 2014. His current research interests include distributed parameter systems, computational intelligence, and robot systems.

Bo Zhuang received his B.S. degree in computer science and education and an M.S. degree in computer science and technology from Shandong Normal University, in 1999 and 2008, respectively. He received his Ph.D. degree in control theory and control engineering from School of IoT Engineering in 2019, Jiangnan University, Wuxi, Jiangsu, China. His current research interests include distributed parameter systems and multiagent systems.

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Bao, C., Cui, B., Wu, W. et al. Boundary Output Feedback for Fixed-time Stabilization of Distributed Parameter Systems With Time and Space Dependent Reactivity. Int. J. Control Autom. Syst. 21, 2516–2528 (2023). https://doi.org/10.1007/s12555-021-1056-2

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  • DOI: https://doi.org/10.1007/s12555-021-1056-2

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