Maximum principle for an optimal control problem associated to a SPDE with nonlinear boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:465

Article

Bonaccorsi, Stefano¹  Zalinescu, Adrian^1,2 

[1] Univ Trento, Dipartimento Matemat, Via Sommar 14, I-38123 Povo, Trento, Italy

[2] Romanian Acad Iasi, O Mayer Math Inst, Carol 1 Blvd,8, Iasi 700506, Romania

关键词: Stochastic control;    Maximum principle;    Stochastic evolution equation;    Backward stochastic differential equation;   

DOI  :  10.1016/j.jmaa.2018.05.016

来源: Elsevier

【 摘 要 】

We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set boundary conditions which result in a stochastic differential equation for the trace of the solution on the boundary. This work provides necessary and sufficient conditions of optimality in the form of a maximum principle. We also provide a result of existence for the optimal control in the case where the control acts linearly. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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