一阶双曲型偏微分方程的模糊边界控制

数学物理学报 ›› 2017, Vol. 37 ›› Issue (3): 469-477.

一阶双曲型偏微分方程的模糊边界控制

熊君, 李俊民, 何超

西安电子科技大学数学与统计学院西安 710126

收稿日期:2016-05-26 修回日期:2016-09-13 出版日期:2017-06-26 发布日期:2017-06-26
通讯作者: 李俊民,E-mail:jmli@mail.xidian.edu.cn E-mail:jmli@mail.xidian.edu.cn
作者简介:熊君,E-mail:junxiongying@163.com;何超,E-mail:xidianhechao@126.com
基金资助:
国家自然科学基金（61573013）

Fuzzy Boundary Control Design for a Class of First-Order Hyperbolic PDEs

Xiong Jun, Li Junmin, He Chao

School of Mathematics and Statistics, Xidian University, Xi'an 710126

Received:2016-05-26 Revised:2016-09-13 Online:2017-06-26 Published:2017-06-26
Supported by:
Supported by the NSFC(61573013)

摘要/Abstract

摘要： 对于一类半线性的双曲型偏微分方程的模糊边界控制问题，通过模糊控制方法，将半线性的偏微分方程系统精确表示为T-S模糊偏微分方程模型.因为控制器仅仅分布于边界上，所以基于T-S模糊偏微分方程模型而设计的模糊边界控制器将更容易执行，并且能够保证闭环系统指数稳定.然后利用Lyapunov方法将给出的闭环系统指数稳定的充分条件转化为求解线性不等式的问题.最后，通过仿真实例说明了模糊边界控制的有效性.

关键词: 非线性双曲偏微分方程, T-S模糊模型, 边界控制, 模糊边界控制, 指数稳定性

Abstract: This paper deals with the problem of fuzzy boundary control design for a class of semi-linear hyperbolic PDEs. A Takagi-Sugeno (T-S) fuzzy PDE model is applied to accurately represent the semilinear hyperbolic PDEs system via fuzzy control approach. Based on the T-S fuzzy PDE model, the fuzzy boundary controllers, which is easily implemented since only boundary actuators are used, are proposed to ensure the exponential stability of the resulting closed-loop system. Sufficient conditions of exponential stabilization are established by employing the Lyapunov direct method and presented in term of standard linear matrix inequalities. Finally, the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of the examples.

Key words: Nonlinear hyperbolic partial differential equations, T-S Fuzzy model, Boundary control, Fuzzy boundary control, Exponential Stability

中图分类号:

O231.4

熊君, 李俊民, 何超. 一阶双曲型偏微分方程的模糊边界控制[J]. 数学物理学报, 2017, 37(3): 469-477.

Xiong Jun, Li Junmin, He Chao. Fuzzy Boundary Control Design for a Class of First-Order Hyperbolic PDEs[J]. Acta mathematica scientia,Series A, 2017, 37(3): 469-477.

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