A feedback control method for the stabilization of a nonlinear diffusion system on a graph

doi:10.1088/1674-1056/23/8/080206

中国物理B ›› 2014, Vol. 23 ›› Issue (8): 80206-080206.doi: 10.1088/1674-1056/23/8/080206

A feedback control method for the stabilization of a nonlinear diffusion system on a graph

于欣^a, 许超^b, 林群^c

a Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
b The State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou 310027, China;
c Department of Mathematics and Statistics, Curtin University, 6845, Australia

收稿日期:2013-10-28 修回日期:2013-11-27 出版日期:2014-08-15 发布日期:2014-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61374096, 61104048, and 11231007) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110751).

A feedback control method for the stabilization of a nonlinear diffusion system on a graph

Yu Xin (于欣)^a, Xu Chao (许超)^b, Lin Qun (林群)^c

a Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
b The State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou 310027, China;
c Department of Mathematics and Statistics, Curtin University, 6845, Australia

Received:2013-10-28 Revised:2013-11-27 Online:2014-08-15 Published:2014-08-15
Contact: Xu Chao E-mail:cxu@zju.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61374096, 61104048, and 11231007) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110751).

摘要/Abstract

摘要： In this paper, we consider the internal stabilization problems of FitzHugh-Nagumo (FHN) systems on the locally finite connected weighted graphs, which describe the process of signal transmission across axons in neurobiology. We will establish the proper condition on the weighted Dirichlet-Laplace operator on a graph such that the nonlinear FHN system can be stabilized exponentially and globally only using internal actuation over a sub-domain with a linear feedback form.

关键词: FitzHugh-Nagumo system, graph, stabilization, internal controller

Abstract: In this paper, we consider the internal stabilization problems of FitzHugh-Nagumo (FHN) systems on the locally finite connected weighted graphs, which describe the process of signal transmission across axons in neurobiology. We will establish the proper condition on the weighted Dirichlet-Laplace operator on a graph such that the nonlinear FHN system can be stabilized exponentially and globally only using internal actuation over a sub-domain with a linear feedback form.

Key words: FitzHugh-Nagumo system, graph, stabilization, internal controller

中图分类号: (Control theory)

02.30.Yy

89.75.-k (Complex systems) 87.10.Ed (Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models)

于欣, 许超, 林群. A feedback control method for the stabilization of a nonlinear diffusion system on a graph[J]. 中国物理B, 2014, 23(8): 80206-080206.

Yu Xin (于欣), Xu Chao (许超), Lin Qun (林群). A feedback control method for the stabilization of a nonlinear diffusion system on a graph[J]. Chin. Phys. B, 2014, 23(8): 80206-080206.

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A feedback control method for the stabilization of a nonlinear diffusion system on a graph

A feedback control method for the stabilization of a nonlinear diffusion system on a graph

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