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Output Feedback Stabilization for a Class of Cascade Nonlinear ODE-PDE Systems

  • Control Theory and Applications
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International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this paper, the output feedback stabilization problem is studied for a class of cascade nonlinear ODE-PDE systems. The nonlinear terms of ODE-subsystem are assumed to be bounded by a known constant multiplied by unmeasured states, and PDE-subsystem is a diffusion equation. Especially, the unstable diffusion equation is considered. Based on the low gain observer and a series of transformations, the output feedback stabilization problem is converted into designing proper gain parameters. Furthermore, the stability of the closed-loop system is analyzed by Lyapunov theorem. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed control strategy.

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Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, 250061, P. R. China

    Yanjie Chang, Xianfu Zhang & Xiandong Chen

  2. School of Mathematics, Shandong University, Jinan, 250100, P. R. China

    Tongjun Sun

Authors
  1. Yanjie Chang
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  2. Tongjun Sun
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  3. Xianfu Zhang
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  4. Xiandong Chen
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Corresponding author

Correspondence to Xianfu Zhang.

Additional information

The work was supported by the National Natural Science Foundation of China (11871312, 62073190 and 61973189), the Foundation for Innovative Research Groups of National Natural Science Foundation of China (61821004), the Natural Science Foundation of Shandong Province of China (ZR2018MA007), and the Research Fund for the Taishan Scholar Project of Shandong Province of China (ts20190905).

Yanjie Chang received her B.S. degree in mathematics and applied mathematics from Hebei GEO University, China, in 2017. Currently, she is pursuing a Ph.D. degree in the School of Control Science and Engineering, Shandong University, China. Her currrent research interests include nonlinear systems and PDE systems.

Tongjun Sun received his B.S. degree in mathematics, his M.E. and Ph.D. degrees in computational mathematics from Shandong University of China in 1994, 1997, and 2000, respectively. He joined the School of Mathematics, Shandong University, China, in 2000, where he is currently a professor. His research interests include numerical methods for PDEs and optimal control problem governed by PDEs, such as finite element method, finite difference method, stochastic Galerkin method.

Xianfu Zhang received his M.S. degree in fundamental mathematics from the School of Mathematics Sciences, Shandong Normal University, China, in 1999, and a Ph.D. degree in operational research and control from the School of Mathematics, Shandong University, China, in 2005. From 1999 to 2011, he worked in the School of Science, Shandong Jianzhu University, China. From September 2008 to February 2009, he was a visiting scholar in the Department of Mechanical Engineering, Ecole Polytechnique de Montreal, Canada. From November 2009 to February 2010, and from July 2012 to October 2012, he was a research assistant in City University of Hong Kong, Hong Kong. He joined the School of Control Science and Engineering, Shandong University, China, in 2012, where he is currently a professor. His main research interests include nonlinear systems, fractional-order systems, and time-delay systems.

Xiandong Chen received his B.S. degree in mathematics from Shandong Jianzhu University, China, in 2014, and an M.S. degree in system analysis and integration from Shandong University, China, in 2017, respectively. He is currently pursuing a Ph.D. degree in the School of Control Science and Engineering, Shandong University, China. His research interests include nonlinear systems and control, time-delay systems and control.

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Chang, Y., Sun, T., Zhang, X. et al. Output Feedback Stabilization for a Class of Cascade Nonlinear ODE-PDE Systems. Int. J. Control Autom. Syst. 19, 2519–2528 (2021). https://doi.org/10.1007/s12555-020-0402-0

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  • DOI: https://doi.org/10.1007/s12555-020-0402-0

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