PDE-ODE无穷维耦合系统的镇定与控制

PDE-ODE无穷维耦合系统的镇定与控制有很强的物理背景和工程应用背景，是分布参数系统理论研究的热点问题之一。对于一个非稳定ODE系统，常见方法是设计PDP位移反馈和时滞位移反馈控制器。由于时滞过程可以看作是一个运输方程，因此，时滞控制下的ODE系统可以看作是由ODE和PDE通过边界连接在一起的无穷维耦合系统。本项目首先考虑控制输入本身具有时滞的二阶ODE系统在PDP反馈控制下的镇定问题，得到系统参数与时滞无关的稳定性区域和与时滞相关的稳定性区域；其次给出ODE系统在热方程补偿下的控制器设计及指数稳定性分析，并且对于同一个非稳定ODE系统，拟给出不同的补偿控制器在研究方法和研究结果方面的差异。. 本项目还将利用MATLAB等数学软件进行模拟仿真，并进行算例分析，为航空航天，化学工程，机器人手臂等工程实践提供强有力的理论支持和指导。

The stabilization and control of PDE-ODE infinite dimensional coupled systems, which have strong backgrounds of physics and engineering application, is a hot topic in the field of distributed parameter control systems. For an unstable ODE system, an usual method is designing the PDP controller. Since the process of time-delay can be described by a transport PDE, an ODE system under a delayed controller can be regarded as an infinite coupled system composed of an ODE and a PDE, which are interconnnected by the boundary. Firstly, the feedback control and stabilization of a second-order ODE are studied when the controller itself has time-delay, and then the delay-independent stability region and delay-dependent stability region are obtained. Secondly, the control design and stability analysis of an ODE under a heat compensator are established. For different compensators, the differences in research techniques and results are concluded.. Simulation results and computational examples with MATLAB software system are presented in order to provide theoretical support for engineering practice, such as aerospace, chemical engineering and robotic arm.