Abstract
An optimal control problem for non-linear stochastic n-order system is treated. The system is subjected to some kind of coloured noise, for which the system's state does not constitute a Markov process. By applying a Girsanov-type transformation a representation and a probability measure are constructed such that the state of the system, in this representation, is a Markov process with respect to the constructed probability measure. Then, by applying calculus of variations, necessary conditions on the optimal control are derived. These conditions are given by a pair of coupled non-linear partial integro-differential equations. However, in order to compute the optimal controls, it is enough to solve only the first one of these equations.
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