论文标题
恒定延迟预测器反馈的鲁棒性，用于随时间和空间变化的反应 - 扩散PDE的内域稳定
Robustness of constant-delay predictor feedback for in-domain stabilization of reaction-diffusion PDEs with time- and spatially-varying input delays
论文作者
论文摘要
本文讨论了在分布式驱动的不确定时间和空间变化的延迟的情况下，反应扩散PDE与罗宾边界条件的反馈反馈稳定。提出的控制设计策略由基于控制输入延迟的已知名义值设计的恒定预测预测反馈组成，并在有限维截断的模型上合成，捕获原始无限二维系统的不稳定模式。通过使用小增益参数，我们表明所得的闭环系统是指数稳定的，只要其名义值的延迟的变化足够小。所提出的证明实际上适用于与无界操作员相关的任何分布式参数系统，即1）在紧凑的间隔上在正方形集成函数的加权空间上生成$ C_0 $ -Semigroup； 2）与紧凑的分辨率是自我伴侣。
This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design strategy consists of a constant-delay predictor feedback designed based on the known nominal value of the control input delay and is synthesized on a finite-dimensional truncated model capturing the unstable modes of the original infinite-dimensional system. By using a small-gain argument, we show that the resulting closed-loop system is exponentially stable provided that the variations of the delay around its nominal value are small enough. The proposed proof actually applies to any distributed-parameter system associated with an unbounded operator that 1) generates a $C_0$-semigroup on a weighted space of square integrable functions over a compact interval; and 2) is self-adjoint with compact resolvent.
