On stationary optimal strategies for team LQG control problems

In the field of decentralized stochastic (team) control, the search for stationary strategies over an infinite time horizon has always represented a challenging and still unsolved problem. For this reason, one is led to consider the application of a receding horizon control scheme. In this case, one must solve at each time instant an optimization problem with constant structure, conditioned to what has taken place in the past. More specifically, the information structure of the team which will be considered in the paper is characterized by two important properties: i) partial nestedness; ii) existence of a common past information set. With these hypotheses, and with reference to a LQG setting of the problem, it has been proven that the receding horizon control scheme yields a linear strategy of constant structure, but with time-varying parameters. This fact is due to the dependence of the solution of the optimization problem from a set of past strategies. The purpose of the paper is to determine necessary conditions for the existence of a decentralized optimal receding horizon stationary strategy.