Decomposed resolution of finite-state aggregative optimal control problems

Kang Liu (1, 2, 3) , Nadia Oudjane (4) , Laurent Pfeiffer (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 L2S - Laboratoire des signaux et systèmes
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 EDF R&D OSIRIS - Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie

A class of finite-state and discrete-time optimal control problems is introduced. The problems involve a large number of agents with independent dynamics, which interact through an aggregative term in the cost function. The problems are intractable by dynamic programming. We describe and analyze a decomposition method that only necessitates to solve at each iteration small-scale and independent optimal control problems associated with each single agent. When the number of agents is large, the convergence of the method to a nearly optimal solution is ensured, despite the absence of convexity of the problem. The procedure is based on a method called Stochastic Frank-Wolfe algorithm, designed for general nonconvex aggregative optimization problems. Numerical results are presented, for a toy model of the charging management of a battery fleet.

Domaines: Optimisation et contrôle [math.OC]

Kang Liu, Nadia Oudjane, Laurent Pfeiffer. Decomposed resolution of finite-state aggregative optimal control problems. 2023 Proceedings of the Conference on Control and its Applications (CT), Jul 2023, Philadelphie (USA), United States. pp.56-63, ⟨10.1137/1.9781611977745.8⟩. ⟨hal-03642127v2⟩