论文标题
网络耦合子系统的最佳控制：光谱分解和低维解
Optimal control of network-coupled subsystems: Spectral decomposition and low-dimensional solutions
论文作者
论文摘要
在本文中，我们研究了对网络耦合子系统的最佳控制，其中动态和成本耦合取决于基本的无向加权图。动力学中的图耦合矩阵可以是邻接矩阵，拉普拉斯矩阵或对应于基础图的任何其他对称矩阵。成本耦合可以是基础耦合矩阵的任何多项式函数。我们使用图耦合矩阵的光谱分解将整个系统分解为具有脱钩动力学和成本的（L+1）系统，其中L是耦合矩阵的等级。此外，可以通过求解（LDIST + 1）解耦Riccati方程来计算每个子系统的最佳控制输入，其中ldist（ldist \ leq l）是耦合矩阵的不同非零特征值的数量。结果的一个显着特征是，解决方案的复杂性取决于耦合矩阵的不同特征值的数量，而不是网络的大小。因此，提出的解决方案框架为大规模网络耦合子系统综合和实施最佳控制法提供了可扩展的方法。
In this paper, we investigate optimal control of network-coupled subsystems where the dynamics and the cost couplings depend on an underlying undirected weighted graph. The graph coupling matrix in the dynamics may be the adjacency matrix, the Laplacian matrix, or any other symmetric matrix corresponding to the underlying graph. The cost couplings can be any polynomial function of the underlying coupling matrix. We use the spectral decomposition of the graph coupling matrix to decompose the overall system into (L+1) systems with decoupled dynamics and cost, where L is the rank of the coupling matrix. Furthermore, the optimal control input at each subsystem can be computed by solving (Ldist + 1) decoupled Riccati equations where Ldist (Ldist \leq L) is the number of distinct non-zero eigenvalues of the coupling matrix. A salient feature of the result is that the solution complexity depends on the number of distinct eigenvalues of the coupling matrix rather than the size of the network. Therefore, the proposed solution framework provides a scalable method for synthesizing and implementing optimal control laws for large-scale network-coupled subsystems.
