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Boundary control for a class of reaction-diffusion systems

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Abstract

Boundary control for a class of partial integro-differential systems with space and time dependent coefficients is considered. A control law is derived via the partial differential equation (PDE) backstepping. The existence of kernel equations is proved. Exponential stability of the closed-loop system is achieved. Simulation results are presented through figures.

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Authors and Affiliations

  1. School of Mathematics and System Science, Southwest University, Chongqing, 400715, China

    Yuan-Chao Si, Cheng-Kang Xie & Na Zhao

  2. School of Mathematics and System Science, Guizhou University, Guiyang, Guizhou, 550025, China

    Yuan-Chao Si

Authors
  1. Yuan-Chao Si
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  2. Cheng-Kang Xie
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  3. Na Zhao
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Corresponding author

Correspondence to Cheng-Kang Xie.

Additional information

Recommended by Associate Editor Zheng-Tao Ding

Yuan-Chao Si received the B. Sc. degree in mathematics and applied mathematics from University of Science and Technology Beijing, China in 2012, and received the M. Sc. degree in operational research and cybernetics from Southwest University, China in 2015.

His research interests include the boundary control of partial differential systems, nonlinear systems, coupled ordinary differential equation and partial differential equation systems.

Cheng-Kang Xie received the B. Sc. degree in mathematics from Southwest University, China, and received the M. Sc. degree in applied mathematics from Yunnan University, China, and received the Ph.D. degree in control engineering from University of Southampton, UK in 2004. He has published more than 50 papers on Systems & Control Letters, International Journal of Control, International Journal of Robust and Nonlinear Control, etc. He is with the School of Mathematics and System Science, Southwest University. He is the head of the Department of Applied Mathematics.

His research interests include distributed parametric systems, especially the boundary control of partial differential systems, and nonlinear systems.

Na Zhao received the B. Sc. degree in mathematics and applied mathematics from Shanxi Normal University, China in 2012, and now is a master student in cybernetics at Southwest University, China.

Her research interests include the boundary control of partial differential systems, coupled ordinary differential equation and partial differential equation systems.

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Si, YC., Xie, CK. & Zhao, N. Boundary control for a class of reaction-diffusion systems. Int. J. Autom. Comput. 15, 94–102 (2018). https://doi.org/10.1007/s11633-016-1012-4

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  • DOI: https://doi.org/10.1007/s11633-016-1012-4

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