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球对称n维反应扩散方程的边界观测与输出反馈控制

齐洁 王川 潘峰

齐洁, 王川, 潘峰. 球对称n维反应扩散方程的边界观测与输出反馈控制. 自动化学报, 2015, 41(7): 1356-1364. doi: 10.16383/j.aas.2015.c140741
引用本文: 齐洁, 王川, 潘峰. 球对称n维反应扩散方程的边界观测与输出反馈控制. 自动化学报, 2015, 41(7): 1356-1364. doi: 10.16383/j.aas.2015.c140741
QI Jie, WANG Chuan, PAN Feng. Boundary Observer and Output-feedback Control for a Class of n-dimensional Symmetric Advection-diffusion Equations. ACTA AUTOMATICA SINICA, 2015, 41(7): 1356-1364. doi: 10.16383/j.aas.2015.c140741
Citation: QI Jie, WANG Chuan, PAN Feng. Boundary Observer and Output-feedback Control for a Class of n-dimensional Symmetric Advection-diffusion Equations. ACTA AUTOMATICA SINICA, 2015, 41(7): 1356-1364. doi: 10.16383/j.aas.2015.c140741

球对称n维反应扩散方程的边界观测与输出反馈控制

doi: 10.16383/j.aas.2015.c140741
基金项目: 

国家自然科学基金(61134009, 61104154), 中央高校基本科研业务费专项资金(2232015D3-24, 2232012D3-19)资助

详细信息
    作者简介:

    王川东华大学信息科学与技术学院硕士研究生. 主要研究方向为偏微分方程边界控制, 多智能体系统协同控制.E-mail: 785407617@qq.com

Boundary Observer and Output-feedback Control for a Class of n-dimensional Symmetric Advection-diffusion Equations

Funds: 

Supported by National Natural Science Foundation of China (61134009, 61104154) and Fundamental Research Funds for the Central Universities (2232015D3-24, 2232012D3-19)

  • 摘要: 许多实际系统可用n 维超球坐标系来描述, 并且系统有球对称的性质, 因而可通过研究半径方向的状态变化, 得到系统的全局动态过程. 通过将高维的对称系统转化为等价的径向一维方程, 本文采用边界Backstepping 方法设计了球对称反应扩散方程的输出反馈控制器. 使用容易测量的边界状态值, 设计了状态观测器来估计系统在空间域的所有状态, 从而实现输出反馈控制. 本文扩展了连续Backstepping 方法,提出了n维球坐标的Volterra 积分映射, 从而求出了显式表达的控制器和状态观测器. 论文用Lyapunov 函数法证明了输出反馈系统在H1范数下指数稳定, 表明状态对初值的连续依赖, 确保控制系统具有较好的性质, 不会在空间某点发散. 最后进行了数值仿真, 仿真结果表明系统在输出反馈控制律的作用下收敛到稳态值.
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出版历程
  • 收稿日期:  2014-10-24
  • 修回日期:  2015-02-27
  • 刊出日期:  2015-07-20

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