2.845

2023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

基于微分方程对称的分布参数系统稳态控制

魏萍 丁卯 左信 罗雄麟

魏萍, 丁卯, 左信, 罗雄麟. 基于微分方程对称的分布参数系统稳态控制. 自动化学报, 2014, 40(10): 2163-2170. doi: 10.3724/SP.J.1004.2014.02163
引用本文: 魏萍, 丁卯, 左信, 罗雄麟. 基于微分方程对称的分布参数系统稳态控制. 自动化学报, 2014, 40(10): 2163-2170. doi: 10.3724/SP.J.1004.2014.02163
WEI Ping, DING Mao, ZUO Xin, LUO Xiong-Lin. Steady-state Control for Distributed Parameter Systems by Symmetry of Differential Equations. ACTA AUTOMATICA SINICA, 2014, 40(10): 2163-2170. doi: 10.3724/SP.J.1004.2014.02163
Citation: WEI Ping, DING Mao, ZUO Xin, LUO Xiong-Lin. Steady-state Control for Distributed Parameter Systems by Symmetry of Differential Equations. ACTA AUTOMATICA SINICA, 2014, 40(10): 2163-2170. doi: 10.3724/SP.J.1004.2014.02163

基于微分方程对称的分布参数系统稳态控制

doi: 10.3724/SP.J.1004.2014.02163
基金项目: 

国家自然科学基金(20976193), 中国石油大学(北京)科研基金资助项目(KYJJ2012-05-31)

详细信息
    作者简介:

    魏萍 中国石油大学(北京) 自动化系讲师. 主要研究方向为非线性系统、分布参数系统和时滞微分系统的稳定性分析与控制. E-mail: helloweiping@163.com

Steady-state Control for Distributed Parameter Systems by Symmetry of Differential Equations

Funds: 

Supported by National Natural Science Foundation of China (20976193), and the Science Foundation of China University of Petroleum (KYJJ2012-05-31)

  • 摘要: 应用对称群理论中经典对称, 以无穷小生成元为分析工具, 考虑分布参数系统的控制问题已有研究, 在此基础上, 本文给出利用微分方程对称实现分布参数系统稳态控制的方法. 通过求解微分方程的对称, 借助其和无穷小生成元之间的关系, 研究给出符合控制目标稳态要求的分布参数系统边界控制条件. 针对两个例子,说明了利用微分方程对称实现分布参数系统稳态控制的过程, 设计了边界控制条件, 进行了仿真说明. 相较基于经典对称获得分布参数系统无穷小生成元的过程, 利用微分方程对称, 避免了空间延拓过程, 并可能获得与其不同的无穷小生成元形式.
  • [1] Padhi R, Ali S F. An account of chronological developments in control of distributed parameter systems. Annual Reviews in Control, 2009, 33(1): 59-68
    [2] [2] Ng J, Dubljevic S. Optimal boundary control of parabolic PDE with time-varying spatial domain. In: Proceedings of the 4th International Symposium on Advanced Control of Industrial Processes. Hangzhou, China: IEEE, 2011. 216-221
    [3] [3] Alessandri A, Gaggero M, Zoppoli R. Feedback optimal control of distributed parameter systems by using finite-dimensional approximation schemes. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(6): 984-995
    [4] [4] Smyshlyaev A, Krstic M. Backstepping observers for a class of parabolic PDEs. Systems Control Letters, 2005, 54(7): 613-625
    [5] [5] Smyshlyaev A, Krstic M. Boundary Control of PDEs: A Course on Backstepping Designs. Philadelphia: Society for Industrial and Applied Mathematics, 2008
    [6] [6] Krstic M, Smyshlyaev A. Adaptive boundary control for unstable parabolic PDEs - Part I: Lyapunov design. IEEE Transactions on Automatic Control, 2008, 53(7): 1575-1591
    [7] [7] Krstic M, Smyshlyaev A. Adaptive control of PDEs. Annual Reviews in Control, 2008, 32(2): 149-160
    [8] [8] Liu W J. Boundary feedback stabilization of an unstable heat equation. SIAM Journal on Control and Optimization, 2004, 42(3): 1033-1043
    [9] [9] Wu H N, Wang J W, Li H X. Exponential stabilization for a class of nonlinear parabolic PDE systems via fuzzy control approach. IEEE Transactions on Fuzzy Systems, 2012, 20(3): 318-329
    [10] Cheng M B, Radisavljevic V, Su W C. Sliding mode boundary control of unstable parabolic PDE systems with parameter variations and matched disturbances. In: Proceedings of the 2009 American Control Conference. St. Louis, MO: IEEE, 2009. 4085-4090
    [11] Cheng M B, Radisavljevic V, Su W C. Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties. Automatica, 2011, 47(2): 381-387
    [12] Tian Chou. Applications of Lie Groups to Differential Equation. Beijing: Science Press, 2001 (田畴. 李群及其在微分方程中的应用. 北京: 科学出版社, 2001)
    [13] Olver P J. Applications of Lie Groups to Differential Equations (2nd edition). New York: Springer, 1993
    [14] Palazoğlu A, Karakaş A. Control of nonlinear distributed parameter systems using generalized invariants. Automatica, 2000, 36(5): 697-703
    [15] Palazoglu A, Karakas A, Godasi S. Control of nonlinear distributed parameter processes using symmetry groups and invariance conditions. Computers and Chemical Engineering, 2002, 26(7-8): 1023-1036
    [16] Wei Ping, Zuo Xin, Zou Lei, Luo Xiong-Lin. Infinitesimal generator for boundary control of Burgers equation. Journal of the Tsinghua University (Science and Technology), 2012, 52(9): 1171-1175 (魏萍, 左信, 邹磊, 罗雄麟. 基于无穷小生成元的Burgers方程的边界控制. 清华大学学报(自然科学版), 2012, 52(9): 1171-1175)
    [17] Tian Chou. Transformation of equations and transformation of symmetries. Acta Mathematicae Applicatae Sinica, 1989, 12(2): 238-249 (田畴. 方程的变换与对称的变换. 应用数学学报, 1989, 12(2): 238-249)
    [18] Tian C. Symmetries and group-invariant solutions of differential equations. Applied Mathematics: Journal of Chinese Universities (Series B), 1994, 9(4): 319-324
    [19] Li Jian, Liu Yun-Gang. Adaptive boundary control for a class of uncertain heat equations. Acta Automatica Sinica, 2012, 38(3): 469-473 (李健, 刘允刚. 一类不确定热方程自适应边界控制. 自动化学报, 2012, 38(3): 469-473)
  • 加载中
计量
  • 文章访问数:  1368
  • HTML全文浏览量:  74
  • PDF下载量:  1064
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-12-31
  • 修回日期:  2014-05-01
  • 刊出日期:  2014-10-20

目录

    /

    返回文章
    返回