Decomposition of large-scale stochastic optimal control problems

¹ EDF R&D, 1, avenue du Général de Gaulle, 92141 Clamart Cedex, France
² ENSTA ParisTech, 32, boulevard Victor, 75739 Paris Cedex 15, France; pierre.carpentier@ensta.fr
³ Université Paris-Est, CERMICS, École des Ponts, Champs sur Marne, 77455 Marne la Vallée Cedex 2, France, also with EDF R&D and ENSTA

Received: 3 March 2009
Accepted: 7 April 2010

Abstract

In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline the framework of our approach and present promising numerical results on a simplified power management problem.