Plenary lecture: Control of distributed-information nonlinear stochastic systems

In engineering and economic systems, many situations may occur, in which a process is influenced by the presence of several decision makers (DM). Different degrees of cooperation and different degrees of distribution of available information among the DM are possible. In this lecture, we consider the case where various DM share different information patterns but they make decisions aimed at the accomplishment of a common goal, i.e., the minimization of the same cost functional. A general approach to the solution of a team optimal decision problem has not yet been presented in the literature. Therefore, in this lecture we give up looking for optimal solutions to a general team optimal control problem, and propose a technique to obtain suboptimal (but approximate to any degree of accuracy) solutions. This is accomplished by constraining the control functions to take on the structure of feedforward neural networks thanks to their powerful approximation capabilities and because these functional structures allow for a simple distributed computation of the local control strategies by stochastic approximation techniques. The neural control methodology is worked out on two important benchmark problems. A simple team within the LQG framework is first considered, where two decision makers with scalar information are present. When the problem admits a known optimal solution, our approach has demonstrated to be able to approximate it. Quite satisfactory results were obtained also in a case (the well-known Witsenhausen counterexample) where the optimal solution has not yet been found (it is however known that it exists). Then, dynamic routing in communication networks is considered. A nonlinear discrete-time dynamic model is given for a store-and-forward packet switching network in which the routing nodes play the role of cooperating DM of a team. The resulting problem does not verify either the LQG hypotheses or the partially nestedness assumption on the information structure.