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基于输出带干扰非线性一维波动方程的输出反馈镇定

张小英1,柴树根2   

  1. 1. 山西农业大学文理学院, 太谷 030801; 2. 山西大学数学科学学院, 太原 030006
  • 出版日期:2019-01-25 发布日期:2019-03-19

张小英,柴树根. 基于输出带干扰非线性一维波动方程的输出反馈镇定[J]. 系统科学与数学, 2019, 39(1): 15-29.

ZHANG Xiaoying, CHAI Shugen. Output Feedback Stabilization of Nonlinear One-Dimensional Wave Equation Under Boundary Output with Disturbance[J]. Journal of Systems Science and Mathematical Sciences, 2019, 39(1): 15-29.

Output Feedback Stabilization of Nonlinear One-Dimensional Wave Equation Under Boundary Output with Disturbance

ZHANG Xiaoying1 ,CHAI Shugen2   

  1. 1. College of Arts and Sciences, Shanxi Agricultural University, Taigu 030801; 2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006
  • Online:2019-01-25 Published:2019-03-19

研究了基于输出带干扰非线性一维波动方程的输出反馈镇定. 首先, 设计时变增益观测器获得干扰的估计. 其次, 使用干扰补偿原则获得输出反馈控制器. 最后, 对闭环系统解的存在性与唯一性作了证明, 进一步使用能量扰动法获得闭环系统的渐近稳定性.

This paper studies the output feedback stabilization for nonlinear one-dimensional wave equation under boundary output with disturbance. Firstly, a time varying gain extended state observer is designed in terms of output to estimate disturbance. Secondly, the output feedback controller is obtained by the principle of interference compensation. Finally, the existence and uniqueness of the classical solution of the closed-loop system is proved and the asymptotical stability of the closed-loop system is obtained by the energy perturbation method by us.

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