Synthesis of the optimal control for linear stochastic dynamical systems with finite aftereffect and poisson disturbances

We obtained the Bellman functional and the optimal control for the problem of control of the linear stochastic system, which is described by the differential-functional equation with finite aftereffect and the Poisson switchings with quadratic functional of performance criterion. For the purpose of determination of the corresponding functions for construction of the Bellman functional and the optimal control we suggested the system of ordinary differential equations, for which we substantiated the existence of unique solution. We stated certain examples of the considered control problem.