On the application of deterministic optimization methods to stochastic control problems

A technique is presented by which one can apply deterministic optimization techniques, for example, the maximum principle of Pontryagin, to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.