Existence of optimal controls for SPDE with locally monotone coefficients. Issue 6 (2nd June 2020)

• Record Type: Journal Article
• Authors: Coayla-Teran, Edson A.; Dias de Magalhães, Paulo M.; Ferreira, Jorge
• Is Part Of: International journal of control. Volume 93:Issue 6(2020)
• Page Start: 1362
• Page End: 1370
• Publication Date: 2020-06-02
• Subjects: Stochastic optimal control -- stochastic partial differential equation -- stochastic systems -- control problems; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1508849
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : The aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotone coefficients controlled by external forces which are feedback controls. To attain our objective we adapt the argument of Lisei (2002) where the existence of optimal controls to the stochastic Navier–Stokes equation was studied. The results obtained in the present paper may be applied to demonstrate the existence of optimal controls to various types of controlled SPDEs such as: a stochastic nonlocal equation and stochastic semilinear equations which are locally monotone equations; we also apply the result to a monotone equation such as the stochastic reaction–diffusion equation and to a stochastic linear equation.