2.624

2020影响因子

(CJCR)

  • 中文核心
  • EI
  • 中国科技核心
  • Scopus
  • CSCD
  • 英国科学文摘

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于反步法的耦合分数阶反应扩散系统边界输出反馈控制

庄波 崔宝同 楼旭阳 陈娟

庄波, 崔宝同, 楼旭阳, 陈娟. 基于反步法的耦合分数阶反应扩散系统边界输出反馈控制. 自动化学报, 2022, 48(11): 2729−2743 doi: 10.16383/j.aas.c190389
引用本文: 庄波, 崔宝同, 楼旭阳, 陈娟. 基于反步法的耦合分数阶反应扩散系统边界输出反馈控制. 自动化学报, 2022, 48(11): 2729−2743 doi: 10.16383/j.aas.c190389
Zhuang Bo, Cui Bao-Tong, Lou Xu-Yang, Chen Juan. Backstepping-based output feedback boundary control for coupled fractional reaction-diffusion systems. Acta Automatica Sinica, 2022, 48(11): 2729−2743 doi: 10.16383/j.aas.c190389
Citation: Zhuang Bo, Cui Bao-Tong, Lou Xu-Yang, Chen Juan. Backstepping-based output feedback boundary control for coupled fractional reaction-diffusion systems. Acta Automatica Sinica, 2022, 48(11): 2729−2743 doi: 10.16383/j.aas.c190389

基于反步法的耦合分数阶反应扩散系统边界输出反馈控制

doi: 10.16383/j.aas.c190389
基金项目: 国家自然科学基金(61807016), 中国博士后科学基金(2018M642160), 高等学校学科创新引智计划(B12018), 江西省青年自然科学基金(20161BAB212032), 江西省教育厅科学技术基金(GJJ181068)资助
详细信息
    作者简介:

    庄波:江南大学物联网工程学院博士研究生. 2008年获得山东师范大学信息科学与工程学院硕士学位. 主要研究方向为分布参数系统控制. 本文通信作者.E-mail: bozhuang@jiangnan.edu.cn

    崔宝同:江南大学物联网工程学院教授. 2003年获得华南理工大学自动化科学与工程学院博士学位. 主要研究方向为复杂系统控制理论与应用.E-mail: btcui@jiangnan.edu.cn

    楼旭阳:江南大学物联网工程学院教授. 2009年获得江南大学控制理论与控制工程专业工学博士学位. 主要研究方向为网络化机电系统的优化与控制, 混杂系统的分析与控制.E-mail: louxy@jiangnan.edu.cn

    陈娟:爱沙尼亚塔林理工大学博士后研究员. 2018年获得江南大学物联网工程学院工学博士学位. 主要研究方向为分数阶分布参数系统的边界控制和边界观测器设计.E-mail: karenchenjuan.student@sina.com

Backstepping-based Output Feedback Boundary Control for Coupled Fractional Reaction-diffusion Systems

Funds: Supported by National Natural Science Foundation of China (61807016), China Postdoctoral Science Foundation (2018M642160), the 111 Project (B12018), Jiangxi Natural Science Foundation Youth Project (20161BAB212032), and Technology Project of Jiangxi Provincial Education Department (GJJ181068)
More Information
    Author Bio:

    ZHUANG Bo Ph.D. candidate at the School of IoT Engineering, Jiangnan University. He received his master degree from Shandong Normal University in 2008. His research interest covers control of distributed parameter systems. Corresponding author of this paper

    CUI Bao-Tong Professor at the School of IoT Engineering, Jiangnan University. He received his Ph.D. degree from the College of Automation Science and Engineering, South China University of Technology in 2003. His research interest covers control theory of complex systems and its applications

    LOU Xu-Yang Professor at the School of IoT Engineering, Jiangnan University. He received his Ph.D. degree in control theory and control engineering from Jiangnan University in 2009. His research interest covers optimization and control of networked electromechanical systems, analysis and control of hybrid systems

    CHEN Juan Post-doctoral fellow at Tallinn University of Technology, Estonia. She received her Ph.D. degree from the School of IoT Engineering, Jiangnan University in 2018. Her research interest covers boundary control and boundary observer design of fractional distributed parameter systems

  • 摘要: 针对具有空间依赖耦合系数的分数阶反应扩散系统, 利用反步法设计了基于观测器的边界输出反馈控制器, 证明了观测增益和控制增益核函数矩阵方程的适定性. 针对误差系统和输出反馈的闭环系统, 利用分数阶Lyapunov方法分析了系统的Mittag-Leffler稳定性, 且利用Wirtinger不等式改进了耦合系统稳定的条件. 当系统具有空间依赖的耦合系数时, 难以求得控制增益和观测增益核函数的解析解, 为此, 给出了核函数偏微分方程的数值解方法. 数值仿真验证了理论结果.
  • 图  1  耦合系统的边界输出反馈控制

    Fig.  1  Output feedback boundary control for coupled systems

    图  2  开环和闭环系统的状态$ L^2 $范数

    Fig.  2  The state $ L^2 $ norm of open-loop and close-loop systems

    图  3  观测增益, 控制增益核函数和控制输入

    Fig.  3  The observer gain and control gain kernel functions, and control input

    图  4  闭环系统状态各状态分量的演变

    Fig.  4  Evolution of state compoments of the close-loop system

    图  5  存在测量噪声的情况

    Fig.  5  The case with measurement noise

    图  6  开环和闭环系统的状态$ L^2 $范数

    Fig.  6  The state $ L^2 $ norm of open-loop and close-loop systems

    图  7  观测增益, 控制增益核函数和控制输入

    Fig.  7  The observer gain and control gain kernel functions, and control input

    图  8  闭环系统的各状态分量

    Fig.  8  Evolution of state compoments of the close-loop system

    图  9  不同控制参数下闭环系统的状态$ L^2 $范数

    Fig.  9  State $ \tilde{c} $-norm of close-loop systems under different control parameters

  • [1] Saxena R K, Mathai A M, Haubold H J. Fractional reactiondiffusion equations. Astrophysics and Space Science, 2006, 305(3):289-296 doi: 10.1007/s10509-006-9189-6
    [2] Henry B I, Langlands T A M, Wearne S L. Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations. Physical Review E, 2006, 74(3):031116 doi: 10.1103/PhysRevE.74.031116
    [3] Podlubny I. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and some of Their Applications. New York: Academic Press, 1999.
    [4] del Castillo-Negrete D, Carreras B A, Lynch V E. Front dynamics in reaction-diffusion systems with Levy flights: a fractional diffusion approach. Physical Review Letters, 2003, 91:018302 doi: 10.1103/PhysRevLett.91.018302
    [5] 张桂梅, 孙晓旭, 刘建新, 储珺. 基于分数阶微分的TV-L1光流模型的图像配准方法研究. 自动化学报, 2017, 43(12):2213-2224

    Zhang Gui-Mei, Sun Xxiao-Xu, Liu Jian-Xin, Chu Jun. Research on TV-L1 optical flow model for image registration based on fractional-order differentiation. Acta Automatica Sinica, 2017, 43(12):2213-2224
    [6] Yin H W, Wen X Q. Pattern formation through temporal fractional derivatives. Scientific Reports, 2018, 8(1):5070 doi: 10.1038/s41598-018-23470-8
    [7] Liu W J. Boundary feedback stabilization of an unstable heat equation. SIAM Journal on Control & Optimization, 2003, 42(3):1033-1043
    [8] Smyshlyaev A, Krstic M. Closed-form boundary state feedbacks for a class of 1-D partial integro-differential equations. IEEE Transactions on Automatic Control, 2004, 49(12): 2185-2202 doi: 10.1109/TAC.2004.838495
    [9] Smyshlyaev A, Krstic M. Backstepping observers for a class of parabolic PDEs. Systems & Control Letters, 2005, 54(7): 613-625
    [10] Smyshlyaev A, Krstic M. On control design for PDEs with space-dependent diffusivity or time-dependent reactivity. Automatica, 2005, 41(9):1601-1608 doi: 10.1016/j.automatica.2005.04.006
    [11] Krstic B M, Smyshlyaev A. Boundary Control of PDEs: A Course on Backstepping Design. Philadelphia: Society for Industrial and Applied Mathematics, 2008.
    [12] Smyshlyaev A. Adaptive Control of Parabolic PDEs. Princeton: Princeton University Press, 2010.
    [13] Baccoli A, Pisano A, Orlov Y. Boundary control of coupled reaction-diffusion processes with constant parameters. Automatica, 2015, 54:80-90 doi: 10.1016/j.automatica.2015.01.032
    [14] Baccoli A, Pisano A. Anticollocated backstepping observer design for a class of coupled reaction-diffusion PDEs. Journal of Control Science and Engineering, 2015, 2015:1-10
    [15] Liu B N, Boutat D, Liu D Y. Backstepping observer-based output feedback control for a class of coupled parabolic PDEs with different diffusions. Systems & Control Letters, 2016, 97:61-69
    [16] Orlov Y, Pisano A, Pilloni A, Usia E. Output feedback stabilization of coupled reaction-diffusion processes with constant parameters. SIAM Journal on Control and Optimization, 2017, 55(6):4112-4155 doi: 10.1137/15M1034325
    [17] Vazquez R, Krstic M. Boundary control of coupled reactionadvection-diffusion systems with spatially-varying coefficients. IEEE Transactions on Automatic Control, 2017, 62(4):2026-2033 doi: 10.1109/TAC.2016.2590506
    [18] Deutscher J, Kerschbaum S. Output regulation for coupled linear parabolic PIDEs. Automatica, 2019, 100:360-370 doi: 10.1016/j.automatica.2018.11.033
    [19] Ge F D, Chen Y Q, Kou C H. Boundary feedback stabilisation for the time fractional-order anomalous diffusion system. IET Control Theory & Applications, 2016, 10(11):1250-1257
    [20] Ge F D, Chen Y Q. Extended Luenberger-type observer for a class of semilinear time fractional diffusion systems. Chaos, Solitons & Fractals, 2017, 102:229-235
    [21] Ge F D, Meurer T, Chen Y. Mittag-Leffler convergent backstepping observers for coupled semilinear subdiffusion systems with spatially varying parameters. Systems & Control Letters, 2018, 122:86-92
    [22] Ge F D, Chen Y Q. Observer design for semilinear time fractional diffusion systems with spatially varying parameters. In: Proceedings of the 2018 International Conference on Fractional Differentiation and Its Applications. Amman, Jordan: SSRN, 2018. [Online], available: http://dx.doi.org/10.2139/ssrn.3281639
    [23] Ge F D, Chen Y Q. Event-triggered boundary feedback control for networked reaction-subdiffusion processes with input uncertainties. Information Sciences, 2019, 476:239-255. doi: 10.1016/j.ins.2018.10.023
    [24] Chen J, Zhuang B, Chen Y Q, Cui B T. Backstepping-based boundary feedback control for a fractional reaction diffusion system with mixed or Robin boundary conditions. IET Control Theory & Applications, 2017, 11(17):2964-2976.
    [25] Chen J, Cui B T, Chen Y Q, Mao L. Backstepping-based observer for output feedback stabilization of a boundary controlled fractional reaction diffusion system. In: Proceedings of the 11th Asian Control Conference. Gold Coast, Australia: IEEE, 2017. 2435−2440
    [26] Chen J, Cui B T, Chen Y Q. Backstepping-based boundary control design for a fractional reaction diffusion system with a space-dependent diffusion coefficient. ISA Transactions, 2018, 80:203-211 doi: 10.1016/j.isatra.2018.04.013
    [27] Chen J, Cui B T, Chen Y Q. Observer-based output feedback control for a boundary controlled fractional reaction diffusion system with spatially-varying diffusivity. IET Control Theory & Applications, 2018, 12(11):1561-1572
    [28] Zhou H C, Guo B Z. Boundary feedback stabilization for an unstable time fractional reaction diffusion equation. SIAM Journal on Control and Optimization, 2018, 56(1):75-101 doi: 10.1137/15M1048999
    [29] Li Y, Chen Y Q, Podlubny I. Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica, 2009, 45(8):1965-1969 doi: 10.1016/j.automatica.2009.04.003
    [30] Li Y, Chen Y Q, Podlubny I. Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Computers & Mathematics with Applications, 2010, 59(5):1810-1821
    [31] Hardy G H, Littlewood J E, Pólya G. Inequalities. 2nd ed. Cambridge, UK: Cambridge University Press, 1988.
    [32] Podlubny I. Fractional-order systems and PIλDµ-controllers. IEEE Transactions on Automatic Control, 1999, 44(1):208-214 doi: 10.1109/9.739144
    [33] Matignon D. Stability results for fractional differential equations with applications to control processing. Computational Engineering in Systems Applications, 1996, 2:963-968
    [34] Aguila-Camacho N, Duarte-Mermoud M A, Gallegos J A. Lyapunov functions for fractional order systems. Communications in Nonlinear Science & Numerical Simulation, 2014, 19(9):2951-2957
    [35] Curtain R F, Zwart H. An Introduction to Infinitedimensional Linear Systems Theory. New York: Springer Science and Business Media, 1995.
    [36] Li H F, Cao J X, Li C P. High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (III). Journal of Computational and Applied Mathematics, 2016, 299:159-175 doi: 10.1016/j.cam.2015.11.037
  • 加载中
图(9)
计量
  • 文章访问数:  91
  • HTML全文浏览量:  36
  • PDF下载量:  56
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-05-20
  • 录用日期:  2019-10-01
  • 网络出版日期:  2022-08-08
  • 刊出日期:  2022-11-22

目录

    /

    返回文章
    返回