  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 different external forces which are
feedback controls. To attain our objective we adapt the argument of H. Lisei,
(Existence of optimal and epsilon-optimal controls for the stochastic Navier -
Stokes equation, Nonlinear Analysis, 51, (2002) 95-118) where the existence of
optimal control to the stochastic Navier-Stokes equation was studied. The
results obtained in the present paper may be applied to demonstrate the
existence of optimal control 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.
