Team Optimal Control Problems

Abstract

We consider discrete-time stochastic optimal control problems over a finite number of decision stages in which several controllers share different information and aim at minimizing a common cost functional. This organization can be described within the framework of “team theory.” Unlike the classical optimal control problems, linear-quadratic-Gaussian hypotheses are sufficient neither to obtain an optimal solution in closed-loop form nor to understand whether an optimal solution exists. In order to obtain an optimal solution in closed-loop form, additional suitable assumptions must be introduced on the “information structure” of the team. The “information structure” describes the way in which each controller’s information vector is influenced by the stochastic environment and by the decisions of the other controllers. Dynamic programming cannot be applied unless the information structure takes particular forms. On the contrary, the “extended Ritz method” (ERIM) can be always applied. The ERIM consists in substituting the admissible functions with fixed-structure parametrized functions containing vectors of “free” parameters. The ERIM is tested in two case studies. The former is the well-known Witsenhausen counterexample. The latter is an optimal routing problem in a store-and-forward packet-switching network.