基于无穷小生成元的Burgers方程的边界控制

Infinitesimal generator for boundary control of Burgers equation

该文首先简要介绍了微分方程的不变性条件,以及偏微分方程无穷小生成元的延拓变换,然后分析了如何利用分布参数系统无穷小生成元,求解符合边界条件控制律的过程。对于描述流体流动的Burgers模型,分别讨论了开环和闭环边界控制问题中控制律的选取。设定系统控制目标和初始条件,通过仿真验证选取恰当的控制参数,实现了系统的控制要求,仿真结果说明了控制方法的有效性。该控制方法可以给出解析形式的控制条件,为实现Burgers方程系统的稳定和控制提供了研究基础。

This paper describes the invariance of differential equations and the prolongation transform of the infinitesimal generator for partial differential equations. Then, the infinitesimal generator is used for boundary control of distributed parameter systems. The boundary control of Burgers equation is given for open loop and closed loop conditions. After setting the initial conditions, the control parameter is chosen to meet the control object in simulations. An analytic control condition is given by the control strategy presented in this paper to provide better stabilization and control of Burgers equation.