An Explicit Dynamic Programming Solution for a Decentralized Two-Player Optimal Linear-Quadratic Regulator

We develop optimal controller synthesis algorithms for decentralized control problems, in which individual subsystems are connected over a network. We consider a simple information structure, consisting of two interconnected linear systems, and construct the optimal controller subject to a decentralization constraint via a novel dynamic programming method. We provide explicit state-space formulae for the optimal controller, and show that each player has to do more than simply estimate the states that they cannot observe. In other words, the simplest separation principle does not hold for this decentralized control problem.