基于微分方程对称的分布参数系统稳态控制

应用对称群理论中经典对称, 以无穷小生成元为分析工具, 考虑分布参数系统的控制问题已有研究, 在此基础上, 本文给出利用微分方程对称实现分布参数系统稳态控制的方法. 通过求解微分方程的对称, 借助其和无穷小生成元之间的关系, 研究给出符合控制目标稳态要求的分布参数系统边界控制条件. 针对两个例子,说明了利用微分方程对称实现分布参数系统稳态控制的过程, 设计了边界控制条件, 进行了仿真说明. 相较基于经典对称获得分布参数系统无穷小生成元的过程, 利用微分方程对称, 避免了空间延拓过程, 并可能获得与其不同的无穷小生成元形式.

Steady-state Control for Distributed Parameter Systems by Symmetry of Differential Equations

The problem of controlling distributed parameter systems has been studied by infinitesimal generators based on classical symmetry in some literature. Motivated by this, the symmetry of differential equations used to realize steady-state control of distributed parameter systems is presented in the paper. After computing the symmetry of the differential equations, the boundary control condition satisfying the control purpose can be obtained by the relationship between the symmetry and infinitesimal generators. The steps to realize the steady-state control of distributed parameter systems are described by two examples, and their effectiveness are shown by simulations. Compared with the process obtaining the infinitesimal generators by classical symmetry, the infinitesimal generators can be obtained without space prolongation, and some new type infinitesimal generators may be found in the process. Furthermore, the methods of designing steady-state control law presented here provide a new branch for the research on controlling distributed parameter systems by symmetry group.