Spatially invariant embeddings of systems with boundaries
Spatially invariant embeddings of systems with boundaries
复制标题
有边界系统的空间不变嵌入
DOI：
10.1109/acc.2016.7526633
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Bassam Bamieh
中科院分区：
文献类型：
--
作者：
J. Epperlein;Bassam Bamieh
考虑一类空间分布的最优控制问题，其中空间域是有边界的有限区间。空间不变系统的最优控制设计程序通常不适用于这种有界空间域。对于具有某些对称性的问题，我们展示了如何使用嵌入应用空间不变技术。在本文中，我们将报告此类“可嵌入”问题。作为一个应用，我们考虑了有限区间上作为偏微分方程的系统的LQR问题，其中有限范围系统的解等于它的空间不变对应物的解加上一个校正边界条件的项。我们还表明，这种分解可以理解为状态反馈增益算子的Toeplitz + Hankel分解，其中Toeplitz部分控制内部域的反馈，而Hankel部分在边界附近提供所需的修正。
We consider certain spatially distributed optimal control problems where the spatial domains are finite intervals with boundaries. The optimal control design procedures for spatially invariant systems are normally not applicable to such bounded spatial domains. For problems that possess certain symmetries, we show how to apply spatially invariant techniques using embeddings. In this note, we report on such “embeddable” problems. As an application, we consider LQR problems for systems posed as PDEs on finite intervals, where it will turn out that the solution for the finite-extent system equals that of its spatially invariant counterpart plus a term that corrects for the boundary conditions. We also show that this decomposition can be understood as a Toeplitz plus Hankel decomposition of the state feedback gain operator, with the Toeplitz part governing the feedback in the interior domain, while the Hankel part provides the needed corrections near the boundaries.