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.

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