Distributionally Robust Model Predictive Control with Output Feedback

An output feedback stochastic model predictive control is proposed in this article for a class of stochastic linear discrete-time systems, in which the uncertainties from external disturbance, measurement noise, and initial state estimation error are all considered. Particularly, the support sets of the uncertainties are unbounded and the distributions are not exactly known. Based on distributionally robust optimization, a deterministic convex reformulation is derived for handling chance constraints. Recursive feasibility and convergence of the algorithm are proven. A numerical example is provided to demonstrate the effectiveness of the proposed method.