典型不确定双曲型PDE-ODE耦合系统控制分析与设计

工程中，许多实际问题的动态都可由双曲型PDE-ODE耦合系统刻画。由于系统不可避免地存在不确定性，本项目计划研究两类典型不确定双曲型PDE-ODE耦合系统的镇定与跟踪控制问题。拟研究系统或带有周期和界均未知的输入扰动，或带有界未知的非周期输入扰动(不必具有光滑性)，亦或带有未知时变参数和未知控制系数。这些特点使得所研究系统更一般且具有更强的不确定性，同时也导致拟定研究问题难以使用现有方法/框架解决。将利用切换自适应方法和时变方法建立强有效的扰动抑制机制，利用基于投影算子和梯度算法的自适应方法提出更强适用性的参数不确定性补偿机制，利用算子半群理论、LaSalle不变原理和Lyapunov稳定性理论发展更具普适性的适定性和稳定性分析方法，进而建立不确定双曲型PDE-ODE耦合系统控制设计与性能分析的新方法，为实现分布参数系统的高精度、高可靠性控制提供新思路和新途径。

In engineering, the dynamics of many practical problems can be described by coupled hyperbolic PDE-ODE systems. This project is devoted to the stabilization and tracking control of two classes of typical uncertain coupled hyperbolic PDE-ODE systems, since uncertainties are inevitable in practice. The systems to be studied allow periodic input disturbances with unknown periods and bounds, non-periodic input disturbances with unknown bounds (do not have to be smooth), unknown time-varying parameters and unknown control coefficients. These characteristics not only make the investigated systems more general and possess more serious uncertainties, but also lead to the considered problems difficult or even cannot be solved by the existing control methods or frameworks. For this, switching adaptive method and time-varying method are adopted to establish a strong and effective disturbance rejection mechanism; adaptive method based on projection operator and gradient algorithm is applied to propose a strong applicable parameter uncertainty compensation mechanism; operator semigroup theory, LaSalle invariance principle and Lyapunov stability theory are used to develop a more general method of well-posedness and stability analysis. Subsequently, new methods are established for the control design and performance analysis of the coupled hyperbolic PDE-ODE systems, which will provide new ideas and new sights to achieve high accuracy and high reliability control of the distributed parameter systems.