A direct method for optimization of stochastic distributed systems

The problem of optimal control for distributed system with stochastic distributed disturbance is considered. A direct method, based on expanding each control function in terms of a complete set of orthonormal basis, is used for the computation of the optimal distributed control with a quadratic performance index. The optimal coefficients of this expansion are found via a simple computational algorithm in terms of the state of the system. An example is given for the distributed control of a single dimensional diffusion process excited by a distributed noise.