论文标题
抽象线性系统稳定中的执行动力补偿
Actuator Dynamics Compensation in Stabilization of Abstract Linear Systems
论文作者
论文摘要
这是四个系列论文的第一部分，目的是针对线性系统执行动力学补偿问题。我们考虑了一种级联抽象线性系统的稳定，该系统对线性系统进行了执行动力学补偿，其中控制植物及其执行器动力学都可以是无限二维的。我们开发了一种系统的方式来通过全州反馈来稳定级联系统。在抽象框架中，建立了所得闭环系统的适当性和指数稳定性。获得了具有部分微分方程（PDE）执行器动力学的普通微分方程（ODE）的补偿器的足够条件。反馈设计基于新颖构建的上限 - 三角形变换，在稳定性分析中不需要Lyapunov功能设计。作为应用，研究了具有输入延迟和带有ode执行器动力学的不稳定热方程的ode，以验证理论结果。进行不稳定热系统的数值模拟以视觉验证所提出的方法。
This is the first part of four series papers, aiming at the problem of actuator dynamics compensation for linear systems. We consider the stabilization of a type of cascade abstract linear systems which model the actuator dynamics compensation for linear systems where both the control plant and its actuator dynamics can be infinite-dimensional. We develop a systematic way to stabilize the cascade systems by a full state feedback. Both the well-posedness and the exponential stability of the resulting closed-loop system are established in the abstract framework. A sufficient condition of the existence of compensator for ordinary differential equation (ODE) with partial differential equation (PDE) actuator dynamics is obtained. The feedback design is based on a novelly constructed upper-block-triangle transform and the Lyapunov function design is not needed in the stability analysis. As applications, an ODE with input delay and an unstable heat equation with ODE actuator dynamics are investigated to validate the theoretical results. The numerical simulations for the unstable heat system are carried out to validate the proposed approach visually.
