一阶双曲型偏微分方程的模糊边界控制  

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

作　　者：熊君[1] 李俊民[1] 何超[1] 

机构地区：[1]西安电子科技大学数学与统计学院,西安710126

出　　处：《数学物理学报（A辑）》2017年第3期469-477,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(61573013)~~

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.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 ac- curately 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.

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. 

分 类 号：O231.4[理学—运筹学与控制论]