输出约束条件下一类热传导方程的边界控制  

Boundary control for an inhomogeneous heat equation with output constraint

作　　者：张爽[1] 李滚[1] ZHANG Shuang;LI Gun(School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China)

机构地区：[1]电子科技大学航空航天学院,四川成都611731

出　　处：《控制理论与应用》2016年第8期1068-1073,共6页Control Theory & Applications

基　　金：国家自然科学基金项目(61403063);中央高校基本科研业务费项目(ZYGX2015J120)资助~~

摘　　要：约束问题普遍存在于物理系统中,如何解决分布参数系统的约束问题还没有有效的方法.本文以一类非齐次的热传导方程作为研究对象,设计了一种新型的边界控制方法来稳定系统状态并解决热传导方程的约束问题.为此首先简要地介绍了由偏微分方程和常微分方程共同描述的热传导方程.然后,在未知的分布式外界扰动的影响下,设计一种新型的基于障碍-积分型李雅普诺夫函数的边界控制方法.此方法是基于原始的分布参数系统模型,没有任何的模型简化,因此有效地避免了溢出不稳定问题.本文采用李雅普诺夫方法证明系统稳定性并保证系统的边界输出约束在一定的范围内.最后采用有限差分法进行仿真验证,仿真结果进一步证明了所提出的边界控制方法的有效性.Constrained problems are commonly existed in the physical system. Unfortunately there is no effective way to solve the constrained problem for distributed parameter systems. In this paper, an inhomogeneous heat equation is studied and a novel boundary control is designed to stabilize the system states and solve the constrained problem for the heat equation. First, the heat equation described by partial differential equation (PDE)-ordinary differential equation (ODE) is briefly introduced. Then, under the effect of unknown distributed disturbance, a novel barrier-integral Lyapunov functional-based method is proposed. The designed method is based on the original distributed parameter system model without any model simplification to avoid the spillover instability problem. Third, Lyapunov’s Direct Method is used to analyze the stability of the closed-loop system and to ensure that the boundary output of the heat equation remains in a constrained space. Finally, extensive simulations are given by using finite difference method. The simulation results further show the effectiveness of the proposed control method.

关 键 词：热传导方程 偏微分方程 边界控制 输出约束 分布参数控制系统 

分 类 号：O175[理学—数学] O231[理学—基础数学]