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/

[1] A. Bensoussan Stochastic maximum principle for distributed parameter systems, J. Franklin Inst., Volume 315 (1983) no. 5–6, pp. 387-406

[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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  • Giuseppina Guatteri; Federica Masiero; Carlo Orrieri Stochastic maximum principle for SPDEs with delay, Stochastic Processes and their Applications, Volume 127 (2017) no. 7, p. 2396 | DOI:10.1016/j.spa.2016.11.007
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  • Bohdan Maslowski; Petr Veverka Sufficient Stochastic Maximum Principle for Discounted Control Problem, Applied Mathematics Optimization, Volume 70 (2014) no. 2, p. 225 | DOI:10.1007/s00245-014-9241-9
  • Qing-xin Meng; Mao-ning Tang A variational formula for controlled backward stochastic partial differential equations and some application, Applied Mathematics-A Journal of Chinese Universities, Volume 29 (2014) no. 3, p. 295 | DOI:10.1007/s11766-014-3156-8
  • Ying Hu Stochastic Maximum Principle, Encyclopedia of Systems and Control (2014), p. 1 | DOI:10.1007/978-1-4471-5102-9_229-1
  • Ruimin Xu; Tingting Wu; Guangchen Wang Mean‐Field Backward Stochastic Evolution Equations in Hilbert Spaces and Optimal Control for BSPDEs, Mathematical Problems in Engineering, Volume 2014 (2014) no. 1 | DOI:10.1155/2014/718948
  • AbdulRahman Al-Hussein Necessary Conditions for Optimality for Stochastic Evolution Equations, Abstract and Applied Analysis, Volume 2013 (2013), p. 1 | DOI:10.1155/2013/469390
  • Marco Fuhrman; Ying Hu; Gianmario Tessitore Stochastic Maximum Principle for Optimal Control of SPDEs, Applied Mathematics Optimization, Volume 68 (2013) no. 2, p. 181 | DOI:10.1007/s00245-013-9203-7
  • Kai Du; Shanjian Tang; Qi Zhang Wm,p-solution (p⩾2) of linear degenerate backward stochastic partial differential equations in the whole space, Journal of Differential Equations, Volume 254 (2013) no. 7, p. 2877 | DOI:10.1016/j.jde.2013.01.013
  • Kai Du; Qingxin Meng A Maximum Principle for Optimal Control of Stochastic Evolution Equations, SIAM Journal on Control and Optimization, Volume 51 (2013) no. 6, p. 4343 | DOI:10.1137/120882433
  • Kai Du; Qingxin Meng Stochastic maximum principle for infinite dimensional control systems, arXiv (2012) | DOI:10.48550/arxiv.1208.0529 | arXiv:1208.0529
  • Kai Du; Qingxin Meng A Maximum Principle for Optimal Control of Stochastic Evolution Equations, arXiv (2012) | DOI:10.48550/arxiv.1206.5495 | arXiv:1206.5495

Cité par 24 documents. Sources : Crossref, NASA ADS

☆ 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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