Deterministic control of stochastic reaction-diffusion equations

<p style='text-indent:20px;'>We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In case multiplicative noise, existence optimal controls and necessary conditions for optimality are derived. additive we obtain a representation gradient cost functional adjoint calculus. The restriction to noise avoids necessity introducing backward SPDE. Based on this novel representation, present probabilistic nonlinear conjugate descent method approximate control, apply our results Schlögl model. We also some analysis in where system differs from system.</p>