Networked control of coupled subsystems: Spectral decomposition and low-dimensional solutions
Shuang Gao, Aditya Mahajan · 2019
In this paper, we investigate optimal networked control of coupled subsystems where the dynamics and the cost couplings depend on an underlying weighted graph. We use the spectral decomposition of the graph adjacency matrix to decompose the overall system into (L+1) systems with decoupled dynamics and cost, where L is the rank of the adjacency matrix. Consequently, the optimal control input at each subsystem can be computed by solving (L+1) decoupled Riccati equations. A salient feature of the result is that the solution complexity depends on the rank of the adjacency matrix rather than the size of the network (i.e., the number of nodes). Therefore, the proposed solution framework provides a scalable method for synthesizing and implementing optimal control laws for large-scale systems.