A full solution to the constrained stochastic closed-loop MPC problem via state and innovations feedback and its receding horizon implementation

In this paper we present a full solution to the closed-loop model predictive control problem intrinsically using an observer and innovations feedback, a structure that turns out to be crucial to find its receding horizon implementation. Closed-loop MPC is a strategy in which a reference feedforward trajectory and a linear time varying feedback map are optimized simultaneously using convex optimization techniques. In this formulation, future disturbances are suppressed in an unconservative way by taking future measurements into account. Due to the finite horizon formulation one is forced to use a receding horizon implementation (as in open-loop model predictive control) and we will reveal how to do so.