  Output-Feedback Stochastic Model Predictive Control based on Stochastic
Optimal Control for nonlinear systems is computationally intractable because of
the need to solve a Finite Horizon Stochastic Optimal Control Problem. However,
solving this problem leads to an optimal probing nature of the resulting
control law, called dual control, which trades off benefits of exploration and
exploitation. In practice, intractability of Stochastic Model Predictive
Control is typically overcome by replacement of the underlying Stochastic
Optimal Control problem by more amenable approximate surrogate problems, which
however come at a loss of the optimal probing nature of the control signals.
While probing can be superimposed in some approaches, this is done
sub-optimally. In this paper, we examine approximation of the system dynamics
by a Partially Observable Markov Decision Process with its own Finite Horizon
Stochastic Optimal Control Problem, which can be solved for an optimal control
policy, implemented in receding horizon fashion. This procedure enables
maintaining probing in the control actions. We further discuss a numerical
example in healthcare decision making, highlighting the duality in stochastic
optimal receding horizon control.
