Nazerian Amirhossein, Bhatta Kshitij, Sorrentino Francesco
Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131 USA.
Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22903 USA.
IEEE Open J Control Syst. 2023;2:24-35. doi: 10.1109/ojcsys.2022.3231553. Epub 2022 Dec 22.
In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is 'exact' in the sense that it preserves all the information about the original system and the objective function. Previous work in this area has focused on strategies that exploit symmetries of the underlying system and of the objective function. Here, instead, we implement the algebraic method of simultaneous block diagonalization of matrices (SBD), which we show provides advantages both in terms of the dimension of the subproblems that are obtained and of the computation time. We provide practical examples with networked systems that demonstrate the benefits of applying the SBD decomposition over the decomposition method based on group symmetries.
在本文中，我们考虑应用于具有大量状态和输入的大规模线性动态系统的最优控制问题（OCP）。我们试图将此类问题简化为一组低维的独立OCP。我们的分解在保留关于原始系统和目标函数的所有信息的意义上是“精确的”。该领域以前的工作集中在利用基础系统和目标函数的对称性的策略上。相反，在这里我们实现了矩阵同时块对角化（SBD）的代数方法，我们证明该方法在获得的子问题的维度和计算时间方面都具有优势。我们提供了网络系统的实际例子，展示了应用SBD分解相对于基于群对称性的分解方法的优势。
