A Stochastic MPC Approach with Application to Iterative Learning

We present a Stochastic Model Predictive Controller for constrained uncertain systems. The proposed framework guarantees recursive feasibility of the controller while ensuring probabilistic constraint satisfaction. Furthermore, we show that the closed loop system converges to a neighborhood of the origin regardless of the disturbance realization. The main contribution of this work is to propose a deterministic reformulation of the chance constraints, where the constraint tightening is constant over the prediction horizon. Therefore, the proposed strategy can be integrated with the recently proposed Leaning Model Predictive Control (LMPC) scheme. The properties of the controller and its integration with the LMPC are discussed in the result section.