Comptes Rendus
no. 13-14
Optimal Control
Stochastic maximum principle for optimal control of SPDEs
[Sur le principe du maximum stochastique pour le contrôle optimal des EDP stochastiques]

Présenté par : the Editorial Board

Marco Fuhrman1 ; Ying Hu2 ; Gianmario Tessitore3
1 Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
2 IRMAR, Université Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France
3 Dipartimento di Matematica, Università di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy
Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 683-688.

Dans cette Note, nous présentons un principe du maximum stochastique pour le contrôle optimal des EDP stochastiques dans le cas général (quand le domaine du contrôle nʼest pas forcément convexe et que le coefficient de diffusion peut contenir la variable de contrôle).

In this Note, we give the stochastic maximum principle for optimal control of stochastic PDEs in the general case (when the control domain need not be convex and the diffusion coefficient can contain a control variable).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.07.009

Marco Fuhrman 1 ; Ying Hu 2 ; Gianmario Tessitore 3

1 Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
2 IRMAR, Université Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France
3 Dipartimento di Matematica, Università di Milano-Bicocca, Via R. Cozzi 53, 20125 Milano, Italy 
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Marco Fuhrman; Ying Hu; Gianmario Tessitore. Stochastic maximum principle for optimal control of SPDEs. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 683-688. doi : 10.1016/j.crma.2012.07.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.07.009/

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[2] Y. Hu; S. Peng Adapted solution of a backward semilinear stochastic evolution equation, Stochastic Anal. Appl., Volume 9 (1991) no. 4, pp. 445-459

[3] Q. Lu; X. Zhang General Pontryagin-type stochastic maximum principle and backward stochastic evolution equations in infinite dimensions, 2012 (preprint) | arXiv

[4] A. Lunardi Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhauser Verlag, Basel, 1995

[5] S. Peng A general stochastic maximum principle for optimal control problems, SIAM J. Control Optim., Volume 28 (1990) no. 4, pp. 966-979

[6] S.J. Tang; X.J. Li Maximum principle for optimal control of distributed parameter stochastic systems with random jumps, Differential Equations, Dynamical Systems, and Control Science, Lecture Notes in Pure and Appl. Math., vol. 152, 1994, pp. 867-890

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☆ Supported by Marie Curie ITN Call: FP7-PEOPLE-2007-1-1-ITN, No. 213841-2: Deterministic and Stochastic Controlled Systems and Applications.

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