Optimal Control of Stochastic Dynamic Systems with Semi-Markov Parameters

The paper considers the generalization of the so-called Markov switching models to the case of generalized semi-Markov switching models, where main model is described by Ito stochastic differential equation. The synthesis problem of the optimal control for a stochastic dynamic system with the semi-Markov parameters is solved. To determine the corresponding functions for Bellman functional and optimal control the system of ordinary differential equations is investigated. The case of linear equations is considered in more detail with closed form of optimal control and corresponding model example.