Distributed Infinite-Horizon Optimal Control of Discrete-Time Linear Systems over Networks

In this paper we consider the distributed infinite-horizon Linear-Quadratic-Gaussian optimal control problem for discrete-time systems over networks. In particular, the feedback controller is composed of local control stations, which receives some measurement data from the plant process and regulates a portion of the input signal. We provide a solution when the nodes have information on the structural data of the whole network but takes 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 (in terms of cost index) when the intermediate consensus steps are sufficiently large.