论文标题
双曲系统边界反馈稳定的扩散和鲁棒性
Diffusion and robustness of boundary feedback stabilization of hyperbolic systems
论文作者
论文摘要
我们考虑了在抗位置和驱动抗位置时，考虑到单输入单输出（SISO）一维线性双曲系统的边界反馈控制问题。输出反馈稳定的主要问题是，它需要动态控制定律，其中包括输出的延迟值（直接或通过状态观察者），这可能对特征速度的无限不确定性可能不稳定。本文的目的是通过解决不稳定的开环系统的反馈稳定来突出该问题的某些特征，该系统由两个互连的传输方程组成，并配有反向定位的边界感应和驱动。主要的贡献是表明，在系统中存在任意的小扩散后，控制延迟不确定性的鲁棒性将立即恢复。我们的分析还表明，扩散对稳定性的影响远非显而易见的问题，即表现出一个替代的简单示例，即扩散的存在具有不稳定的效果。
We consider the problem of boundary feedback control of single-input-single-output (SISO) one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The main issue of the output feedback stabilization is that it requires dynamic control laws that include delayed values of the output (directly or through state observers) which may not be robust to infinitesimal uncertainties on the characteristic velocities. The purpose of this paper is to highlight some features of this problem by addressing the feedback stabilization of an unstable open-loop system which is made up of two interconnected transport equations and provided with anti-located boundary sensing and actuation. The main contribution is to show that the robustness of the control against delay uncertainties is recovered as soon as an arbitrary small diffusion is present in the system. Our analysis also reveals that the effect of diffusion on stability is far from being an obvious issue by exhibiting an alternative simple example where the presence of diffusion has a destabilizing effect instead.
