  We revisit closed-loop performance guarantees for Model Predictive Control in
the deterministic and stochastic cases, which extend to novel performance
results applicable to receding horizon control of Partially Observable Markov
Decision Processes. While performance guarantees similar to those achievable in
deterministic Model Predictive Control can be obtained even in the stochastic
case, the presumed stochastic optimal control law is intractable to obtain in
practice. However, this intractability relaxes for a particular instance of
stochastic systems, namely Partially Observable Markov Decision Processes,
provided reasonable problem dimensions are taken. This motivates extending
available performance guarantees to this particular class of systems, which may
also be used to approximate general nonlinear dynamics via gridding of state,
observation, and control spaces. We demonstrate applicability of the novel
closed-loop performance results on a particular example in healthcare decision
making, which relies explicitly on the duality of the control decisions
associated with Stochastic Optimal Control in weighing appropriate appointment
times, diagnostic tests, and medical intervention for treatment of a disease
modeled by a Markov Chain.
