Existence of ϵ-optimal feedback controls for SPDEs with locally monotone coefficients

Abstract This paper aims to investigate the existence of ϵ-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 reach our objective, we use the finite-dimensional method. Furthermore, to illustrate the applicability of the result, we give some examples.