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Dynamic H∞ Feedback Boundary Control for a Class of Parabolic Systems with a Spatially Varying Diffusivity

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  • Control Theory and Applications
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Abstract

The dynamic H∞ feedback boundary control for a class of parabolic distributed parameter systems with a non-constant (spatially varying) diffusion rate is addressed in this paper. The observer-based controller is designed to deal with non-collocated sensors and actuators, and the H∞ performance index is employed to tackle the influence of the external disturbance and measurement noise. The resulting closed-loop system is formed by the boundary actuation with the H∞ control strategy, and the output feedback is designed from the domain-averaged and boundary-valued measurement, respectively. With the sufficient conditions of the linear matrix inequality that infer the stability of the system, the corresponding gains of observer and controller are solved. Numerical simulations are given to show the validity of the main results.

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Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, No. 1800 Lihu Avenue, Wuxi, 214122, P. R. China

    Yanjiu Zhou, Baotong Cui & Xuyang Lou

  2. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 2V4, Canada

    Yanjiu Zhou

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  1. Yanjiu Zhou
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Correspondence to Yanjiu Zhou.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Wei He under the direction of Editor-in-Chief Keum-Shik Hong. This work is supported by China Postdoctoral Science Foundation (2018M642160) and the 111 Project (B12018).

Yanjiu Zhou received her Bachelor’s degree in electric information engineering from Nanjing Forestry University, Nanjing, China, in June 2016. From September 2016, she is pursuing a Ph.D. degree at Jiangnan University. She is currently a Joint Training Ph.D. Student at the Department of Chemical & Materials Engineering, University of Alberta, from June 2019. Her research interests include distributed parameter systems, boundary control, robust control and stability of dynamical systems.

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, China in July 2003. He was a post-doctoral fellow at Shanghai Jiao-Tong University, China, from July 2003 to September 2005, and a visiting scholar at the Department of Electrical and Computer Engineering, National University of Singapore, Singapore, from August 2007 to February 2008. He became an associate professor in December 1993 and a full professor in November 1995 at the Department of Mathematics, Binzhou University, China. He joined Jiangnan University, China in June 2003, where he is a full professor for the School of IoT Engineering. His current research interests include systems analysis, control of distributed parameter systems, stability of dynamical systems, artificial neural networks, and chaos synchronization.

Xuyang Lou received his Ph.D. degree in control theory and control engineering from Jiangnan University, Wuxi, China, in 2009. In 2010, he joined the School of Communication and Control Engineering, Jiangnan University. From October 2007 to October 2008, he was a visiting scholar in the CSIRO Division of Mathematical and Information Sciences, Adelaide, Australia. From July to November 2010, he was a Postdoctoral Fellow in the Department of Electrical Engineering (ESAT-SCDSISTA), Katholieke Universiteit Leuven. From July 2014 to February 2015, he visited the Computer Engineering Department, University of California, Santa Cruz, USA. He is currently a Professor with Jiangnan University. His current research interests include hybrid systems, distributed parameter systems and computational intelligence.

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Zhou, Y., Cui, B. & Lou, X. Dynamic H∞ Feedback Boundary Control for a Class of Parabolic Systems with a Spatially Varying Diffusivity. Int. J. Control Autom. Syst. 19, 999–1012 (2021). https://doi.org/10.1007/s12555-019-0926-3

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