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.

Decomposition of Convex High Dimensional Aggregative Stochastic Control Problems / Seguret, A.; Alasseur, C.; Bonnans, J. F.; De Paola, A.; Oudjane, N.; Trovato, V.. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - 2023, 88:8:1(2023), pp. 1-35. [10.1007/s00245-023-09977-1]

Decomposition of Convex High Dimensional Aggregative Stochastic Control Problems

Trovato V.
2023-01-01

Abstract

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.
2023
1
Seguret, A.; Alasseur, C.; Bonnans, J. F.; De Paola, A.; Oudjane, N.; Trovato, V.
Decomposition of Convex High Dimensional Aggregative Stochastic Control Problems / Seguret, A.; Alasseur, C.; Bonnans, J. F.; De Paola, A.; Oudjane, N.; Trovato, V.. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - 2023, 88:8:1(2023), pp. 1-35. [10.1007/s00245-023-09977-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/404829
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