Optimality Condition for the Receding Horizon Control of Markov Jump Linear Systems with Non-observed Chain and Linear Feedback Controls

We demonstrate here that a necessary condition of optimality studied in a previous paper is in fact a necessary and sufficient condition of optimality for the receding horizon control problem of discrete-time Markov jump linear systems subject to noisy inputs. The performance index is quadratic and the information available to the controller does not involve observations of Markov chain states. Seqyebces of linear feedback gains that are independent of the Markov state is adopted, in accordance with the information available to the controller. We make use of an equivalent deterministic form of expressing the stochastic problem, and the complete solution given in feedback form, is obtained by dynamic programming arguments and by the benefit of some quadratic convex relations.