Optimal Controller Synthesis for Decentralized Systems over Graphs via Spectral Factorization

In this paper, controller synthesis algorithms are developed for decentralized control problems. The distributed systems considered here are represented by graphs, which impose sparsity constraints on the set of allowable controllers. A spectral factorization approach is used to construct the optimal decentralized controllers. Explicit state-space solutions are provided for this class of systems, which establishes the order for the optimal policies. In addition, this work provides an intuitive understanding of the optimal solution. In particular, the standard separation principle does not hold for these decentralized problems, and the controllers must do more than simply estimate their states.