Boundary control of coupled reaction-diffusion systems with spatially-varying reaction

被引:6
|
作者
Vazquez, Rafael [1 ]
Krstic, Miroslav [2 ]
机构
[1] Univ Seville, Dept Aerosp Engn, Camino Descubrimiento SN, Seville 41092, Spain
[2] Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA
来源
IFAC PAPERSONLINE | 2016年 / 49卷 / 08期
关键词
STABILIZATION; EQUATION; PDES;
D O I
10.1016/j.ifacol.2016.07.445
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with spatially-varying reaction (i.e., reaction coefficient depending on the spatial coordinate) is challenging due to complex boundary conditions that appear in the equations verified by the control kernels. In this paper we address this issue by showing that these equations are essentially equivalent to those verified by the control kernels for first-order hyperbolic coupled systems, which were recently found to be well-posed. The result therefore applies in this case, allowing us to prove H1 stability for the closed-loop system. It also shows an interesting connection between backstepping kernels for coupled parabolic and hyperbolic problems. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
引用
收藏
页码:222 / 227
页数:6
相关论文
共 50 条
  • [21] Stabilization of a spatially non-causal reaction-diffusion equation by boundary control
    Guo, C.
    Xie, C.
    Zhou, C.
    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2014, 24 (01) : 1 - 17
  • [22] Boundary Stabilization and H∞ Control for Stochastic Reaction-Diffusion Systems
    Pan, Pei-Liang
    Wang, Jian
    Wu, Kai-Ning
    PROCEEDINGS OF THE 28TH CHINESE CONTROL AND DECISION CONFERENCE (2016 CCDC), 2016, : 2279 - 2283
  • [23] Reaction-diffusion systems coupled at the boundary and the Morse-Smale property
    Broche, Rita de Cassia D. S.
    de Oliveira, Luiz Augusto F.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 245 (05) : 1386 - 1411
  • [24] Synchronization of stochastic reaction-diffusion systems via boundary control
    Wu, Kai-Ning
    Wang, Jian
    Lim, Cheng-Chew
    NONLINEAR DYNAMICS, 2018, 94 (03) : 1763 - 1773
  • [25] Boundary Control for a Class of Reaction-diffusion Systems附视频
    YuanChao Si
    ChengKang Xie
    Na Zhao
    International Journal of Automation and Computing, 2018, (01) : 94 - 102
  • [26] Global existence for coupled reaction-diffusion systems with Dirichlet boundary conditions
    Yang, WL
    Tian, HY
    DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2006, 13 (01): : 77 - 84
  • [27] Boundary control of stochastic reaction-diffusion systems with Markovian switching
    Han, Xin-Xin
    Wu, Kai-Ning
    Ding, Xiaohua
    Yang, Baoqing
    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2020, 30 (10) : 4129 - 4148
  • [28] CONTINUOUSLY VARYING EXPONENTS IN REACTION-DIFFUSION SYSTEMS
    NEWMAN, TJ
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (06): : L183 - L190
  • [29] An observer for an occluded reaction-diffusion system with spatially varying parameters
    Kramer, Sean
    Bollt, Erik M.
    CHAOS, 2017, 27 (03)
  • [30] Backstepping-based Output Feedback Boundary Control for Coupled Fractional Reaction-diffusion Systems
    Zhuang B.
    Cui B.-T.
    Lou X.-Y.
    Chen J.
    Zidonghua Xuebao/Acta Automatica Sinica, 2022, 48 (11): : 2729 - 2743