Distributed Optimal Control of Discrete-Time Linear Systems Over Networks

In this paper we consider the distributed Linear-Quadratic-Gaussian optimal control problem for discrete-time systems over networks. In particular, the feedback controller is composed of local control stations which receive some measurement data from the plant process and regulate a portion of the input signal. We provide a solution when the nodes have information on the structural data of the whole network but take local actions, and also when only local information on the network are available to the nodes. The proposed solution is arbitrarily close to the optimal centralized one when the intermediate number of consensus steps is sufficiently large.