Decomposition of convex high dimensional aggregative stochastic control problems

Adrien Seguret (1, 2) , Clémence Alasseur (3, 1) , Joseph Frédéric Bonnans (4, 5) , Antonio de Paola (6) , Nadia Oudjane (1) , Vincenzo Trovato (6, 7)

1 EDF R&D OSIRIS - Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 FiME Lab - Laboratoire de Finance des Marchés d'Energie
4 DISCO - Dynamical Interconnected Systems in COmplex Environments
5 L2S - Laboratoire des signaux et systèmes
6 DEEE - Department of Electrical and Electronic Engineering [London]
7 Department of civil, environmental and mechanical engineering [Trento]

We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first contribution, we introduce a modified problem, whose optimal control is under some reasonable assumptions an ε-optimal solution of the original problem. As second contribution, we present a decentralized algorithm whose convergence to the solution of the modified problem is established. Finally, we study the application of the developed tools in an engineering context, studying a coordination problem for large populations of domestic thermostatically controlled loads (TCLs).

Mots clés: Stochastic optimization; Lagrangian decomposition; Uzawa's algorithm; Stochastic gradient

Domaines: Optimisation et contrôle [math.OC]; Energie électrique

Adrien Seguret, Clémence Alasseur, Joseph Frédéric Bonnans, Antonio de Paola, Nadia Oudjane, et al.. Decomposition of convex high dimensional aggregative stochastic control problems. Applied Mathematics and Optimization, 2023, 88 (8), pp.35. ⟨10.1007/s00245-023-09977-1⟩. ⟨hal-02917014v5⟩