论文标题
具有动态边界的1D波PDE的输出反馈指数稳定
Output Feedback Exponential Stabilization for a 1-d Wave PDE with Dynamic Boundary
论文作者
论文摘要
我们研究具有动态边界的1D波PDE的输出反馈指数稳定。只有一个测量值，我们构建了一个无限维状态观察者，以追踪状态并设计一个估计的基于状态的控制器，以指数稳定原始系统。对于存在文献而言，这本质上是重要的改进[Ö。 Morgül，B.P。 Rao和F. Conrad，《自动控制的IEEE交易》，39（10）（1994），2140-2145]，其中采用了包括高阶角速度反馈在内的两项测量。当考虑到对照匹配的非线性内部不确定性和外部干扰时，我们构建了无限维度扩展状态观察者（ESO），以同时估计总干扰和状态。通过补偿总干扰，估计的基于状态的控制器旨在指数稳定原始系统，同时使闭环系统有限。 Riesz基础方法对于验证闭环系统两个耦合系统的指数稳定性至关重要。提出了一些数值模拟以说明有效性。
We study the output feedback exponential stabilization for a 1-d wave PDE with dynamic boundary. With only one measurement, we construct an infinite-dimensional state observer to trace the state and design an estimated state based controller to exponentially stabilize the original system. This is an essentially important improvement for the existence literature [Ö. Morgül, B.P. Rao and F. Conrad, IEEE Transactions on Automatic Control, 39(10) (1994), 2140-2145] where two measurements including the high order angular velocity feedback were adopted. When a control matched nonlinear internal uncertainty and external disturbance are taken into consideration, we construct an infinite-dimensional extended state observer (ESO) to estimate the total disturbance and state simultaneously. By compensating the total disturbance, an estimated state based controller is designed to exponentially stabilize the original system while making the closed-loop system bounded. Riesz basis approach is crucial to the verifications of the exponential stabilities of two coupled systems of the closed-loop systems. Some numerical simulations are presented to illustrate the effectiveness.
