Stochastic Model Predictive Control: Output-Feedback, Duality and Guaranteed Performance

A new formulation of Stochastic Model Predictive Output Feedback Control is presented and analyzed as a translation of Stochastic Optimal Output Feedback Control into a receding horizon setting. This requires lifting the design into a framework involving propagation of the conditional state density, the information state, via the Bayesian Filter and solution of the Stochastic Dynamic Programming Equation for an optimal feedback policy, both stages of which are computationally challenging in the general, nonlinear setup. The upside is that the clearance of three bottleneck aspects of Model Predictive Control is connate to the optimality: output feedback is incorporated naturally; dual regulation and probing of the control signal is inherent; closed-loop performance relative to infinite-horizon optimal control is guaranteed. While the methods are numerically formidable, our aim is to develop an approach to Stochastic Model Predictive Control with guarantees and, from there, to seek a less onerous approximation. To this end, we discuss in particular the class of Partially Observable Markov Decision Processes, to which our results extend seamlessly, and demonstrate applicability with an example in healthcare decision making, where duality and associated optimality in the control signal are required for satisfactory closed-loop behavior.