Decomposition of High Dimensional Aggregative Stochastic Control Problems
| Autor: | Seguret, Adrien, Alasseur, Clémence, Frédéric Bonnans, J, De Paola, Antonio, Oudjane, Nadia, Trovato, Vincenzo |
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| Přispěvatelé: | Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie (EDF R&D OSIRIS), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de Finance des Marchés d'Energie (FiME Lab), EDF (EDF)-EDF (EDF)-CREST-Université Paris Dauphine-PSL, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Department of Electrical and Electronic Engineering [London] (DEEE), Imperial College London, Department of civil, environmental and mechanical engineering [Trento], University of Trento [Trento], The first, second, third and fifth author thank the FiME Lab (Institut Europlace deFinance). The third author was supported by the PGMO project 'Optimal control of conservationequations', itself supported by iCODE(IDEX Paris-Saclay) and the Hadamard Mathematics LabEx., Université Paris Dauphine-PSL-CREST-EDF R&D (EDF R&D), Controle, Optimisation, modèles, Méthodes et Applications pour les Systèmes Dynamiques non linéaires (COMMANDS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Bath, Center for Sustainable Power Distribution, Imperial College London, Electrical and Electronic Engineering Department, Center for Sustainable Power Distribution [Bath] (CSPD), University of Bath [Bath], Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-CREST-EDF R&D (EDF R&D) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
90C39
65K10 90C15 13 AMS subject classifications : 93E20 65K10 90C25 90C39 90C15 Stochastic optimization [SPI.NRJ]Engineering Sciences [physics]/Electric power stochastic 11 gradient 12 AMS subject classifications 93E20 93E20 65K10 90C25 90C39 90C15 [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] stochastic gradient 90C25 Uzawa's algorithm Lagrangian decomposition |
| Popis: | We consider the framework of high dimensional stochastic control problem, 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 to a problem of coordination of energy consumption and production of domestic appliances. |
| Databáze: | OpenAIRE |
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