Stochastic Programming Applied to Model Predictive Control

Many robust model predictive control (MPC) schemes are based on min-max optimization, that is, the future control input trajectory is chosen as the one which minimizes the performance due to the worst disturbance realization. In this paper we take a different route to solve MPC problems under uncertainty. Disturbances are modelled as random variables and the expected value of the performance index is minimized. The MPC scheme that can be solved using Stochastic Programming (SP), for which several efficient solution techniques are available. We show that this formulation guarantees robust constraint fulfillment and that the expected value of the optimum cost function of the closed loop system decreases at each time step.