论文标题
运算符值的内核和无限尺寸动态系统的控制
Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems
论文作者
论文摘要
可以说是控制理论中最经典问题的线性二次调节器（LQR）最近与有限尺寸系统（Aubin-Frankowski，Sicon，2021）中的内核方法有关。我们表明，该结果扩展到无限尺寸系统，即\线性偏微分方程的控制。二次物镜与线性动力学配对，编码相关的内核，定义了受控轨迹的希尔伯特空间，为此，我们基于差分方程的解决方案获得了简洁的公式。这为应用内核方法的代表定理的方式铺平了道路，以解决无限的尺寸最佳控制问题。
The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in (Aubin-Frankowski, SICON, 2021) for finite dimensional systems. We show that this result extends to infinite dimensional systems, i.e.\ control of linear partial differential equations. The quadratic objective paired with the linear dynamics encode the relevant kernel, defining a Hilbert space of controlled trajectories, for which we obtain a concise formula based on the solution of the differential Riccati equation. This paves the way to applying representer theorems from kernel methods to solve infinite dimensional optimal control problems.
