Stabilization of an ODE-PDE cascaded system is considered in this paper. The PDE subsystem consists of a system of heat equations, and a control input is set on a boundary. The ODE subsystem is a normal control system cascaded with the PDE subsystem at another boundary, in which its control input is the heat flow rate of the PDE subsystem at this boundary. A boundary control law is constructed by PDE backstepping procedure and lots of complicated mathematical computations. Experiential stability of the closed loop is achieved under this control law.

中文翻译：

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通过边界控制稳定ODE-PDE级联系统

本文考虑了ODE-PDE级联系统的稳定性。PDE子系统由一个热方程系统组成，并且控制输入设置在边界上。ODE子系统是在另一个边界与PDE子系统级联的常规控制系统，其控制输入是该边界处PDE子系统的热流率。边界控制律是通过PDE反推程序和许多复杂的数学计算构造的。根据该控制定律，可以实现闭环的经验稳定性。