Optimal control of systems governed by stochastic McShane differential equations with fixed terminal time

In this paper we consider a class of stochastic systems governed by McShane stochastic differential equations for which both parameters and controls are to be chosen optimally with respect to a certain performance criterion over a fixed time interval. It is shown that this problem can be converted into an equivalent optimization problem of distributed parameter systems of parabolic type with a Cauchy boundary condition. For this reduced problem a necessary condition for optimality is given. This result is then used to obtain the individual necessary conditions for optimal controls and optimal parameters. Finally, a bang—bang principle is shown to hold true for n class of linear optimal control problems.