论文标题
耦合线性抛物线ode-pde-ode系统的输出反馈控制
Output Feedback Control of Coupled Linear Parabolic ODE-PDE-ODE Systems
论文作者
论文摘要
本文介绍了基于观察者的抛物线ode-pde-ode系统的基于观察者的补偿器的后台设计。后者由N偶联的抛物线PDE组成，具有不同的扩散系数和空间变化的系数，它们在两个边界上都与ODES偶联。这些驱动和传感通过这些ODE出现，导致了一个具有挑战性的控制问题。为了确定状态反馈控制器和观察者，为此设置了一种系统的后退方法。特别是，通过使用一系列转换序列，将状态反馈循环和观察者误差动力学映射到稳定的ODE-PDE-ODE CASCADES中。这样，设计可以追溯到文献中已经找到的内核方程的解决方案以及可以通过数值求解的初始和边界值问题。验证了闭环系统的指数稳定性，其中可以在设计中直接指定衰减速率。本文的结果通过具有两个耦合抛物线PDE的不稳定ODE-PDE-ODE系统的输出反馈控制来说明。
This paper deals with the backstepping design of observer-based compensators for parabolic ODE-PDE-ODE systems. The latter consist of n coupled parabolic PDEs with distinct diffusion coefficients and spatially-varying coefficients, that are bidirectionally coupled to ODEs at both boundaries. The actuation and sensing appears through these ODEs resulting in a challenging control problem. For this setup a systematic backstepping approach is proposed, in order to determine a state feedback controller and an observer. In particular, the state feedback loop and the observer error dynamics are mapped into stable ODE-PDE-ODE cascades by making use of a sequence of transformations. With this, the design can be traced back to the solution of kernel equations already found in the literature as well as initial and boundary value problems, that can be solved numerically. Exponential stability of the closed-loop system is verified, wherein the decay rate can be directly specified in the design. The results of the paper are illustrated by the output feedback control of an unstable ODE-PDE-ODE system with two coupled parabolic PDEs.
