DETERMINISTIC CONTROL OF STOCHASTIC REACTION-DIFFUSION EQUATIONS

We consider the control of semilinear stochastic partial differen-tial equations (SPDEs) via deterministic controls. In the case of multiplicative noise, existence of optimal controls and necessary conditions for optimality are derived. In the case of additive noise, we obtain a representation for the gradient of the cost functional via adjoint calculus. The restriction to determin-istic controls and additive noise avoids the necessity of introducing a backward SPDE. Based on this novel representation, we present a probabilistic nonlinear conjugate gradient descent method to approximate the optimal control, and apply our results to the stochastic Schlogl model. We also present some analy-sis in the case where the optimal control for the stochastic system differs from the optimal control for the deterministic system.