基于切换补偿机制的耦合PDE-ODE系统控制

现代控制工程中的许多动态过程可以建模成耦合PDE-ODE系统。由于实际控制过程中不确定性不可避免，研究不确定耦合PDE-ODE系统的控制问题具有重要意义。本项目计划研究四类典型不确定耦合PDE-ODE系统的镇定和输出跟踪控制问题。每类系统均含有输入扰动或未知参数，PDE子系统由热或波方程描述，以不同的方式与ODE子系统耦合。与相关文献相比，未知参数和扰动都不必属于已知有界区间，扰动不必是谐波型的或连续的，因而具有更强的不确定性，导致拟定的科学问题难以使用现有方法/框架解决。将利用切换补偿机制克服不确定性，并结合无穷维反推方法、分布参数系统控制器/观测器设计方法等建立具有更强不确定性的耦合PDE-ODE系统控制设计和性能分析的新框架。本项目所提出的基于切换补偿机制的控制设计方法将为现有框架难以解决的问题提供新思路和新途径，丰富和发展分布参数系统控制理论。

Many dynamic processes can be modeled as coupled PDE-ODE systems in modern control engineering. Since uncertainties ineluctably exist in practice, it is meaningful to investigate the control of uncertain coupled PDE-ODE systems. This project is devoted to the stabilization and output tracking control of four typical classes of coupled PDE-ODE systems. Input disturbances or unknown parameters are involved in each class of systems, wherein PDE subsystems are described by heat or wave equations and coupled with ODE subsystems in different forms. Comparing with the related literature, both the unknown parameters and disturbances do not necessarily belong to known bounded intervals, and simultaneously, the disturbances may not be harmonic or continuous, and hence more serious uncertainties are existing which make the scientific problems investigated in this project difficult to solve by existing methods/frameworks. The switching compensation scheme is adopted to overcome the more serious uncertainties, by which, infinite-dimensional backstepping method and the constructive methods of controller/observer for distributed parameter systems, new frameworks are established for the control design and performance analysis of coupled PDE-ODE systems with more serious uncertainties. The control design methods using switching compensation scheme proposed in this project, will provide new ideas and new sights for the scientific problems which are difficult to solve by the existing frameworks, enrich and develop the control theory of distributed parameter systems.