Dynamic Programming and Minimum Principles for Systems with Jump Markov Disturbances

This paper studies optimum control of random differential equations of the form \[ x = fʳ⁽ᵗ⁾ (t,x,u)\] in which $r(t)$ is a jump Markov process. Optimality conditions of dynamic programming type and stochastic minimum principles are given. The problems posed involve terminal conditions, and transversality conditions are shown to hold.