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. © 2018 Elsevier Inc. All rights reserved.

Maximum principle for an optimal control problem associated to a SPDE with nonlinear boundary conditions / Bonaccorsi, Stefano; Zălinescu, Adrian. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 2018, 465:1(2018), pp. 359-378. [10.1016/j.jmaa.2018.05.016]

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

Bonaccorsi, Stefano;Zălinescu, Adrian
2018

Abstract

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. © 2018 Elsevier Inc. All rights reserved.
1
Bonaccorsi, Stefano; Zălinescu, Adrian
Maximum principle for an optimal control problem associated to a SPDE with nonlinear boundary conditions / Bonaccorsi, Stefano; Zălinescu, Adrian. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 2018, 465:1(2018), pp. 359-378. [10.1016/j.jmaa.2018.05.016]
File in questo prodotto:
File Dimensione Formato  
Control for SPDE with nonlinear dynamical boundary conditions.pdf

accesso aperto

Descrizione: Articolo su Arxiv
Tipologia: Pre-print non referato (Non-refereed preprint)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 376.86 kB
Formato Adobe PDF
376.86 kB Adobe PDF Visualizza/Apri
1-s2.0-S0022247X18304098-main.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 423.78 kB
Formato Adobe PDF
423.78 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/218549
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact