A probabilistic approach to Model Predictive Control

This paper presents a novel Model Predictive Control (MPC) algorithm for linear systems subject to stochastic noise and probabilistic constraints on the state and control variables. The method is based on the reformulation of these constraints in terms of deterministic ones, on the use of terminal constraints on the mean value and on the covariance of the state, and on a binary strategy for the selection of the initial conditions to be considered at any time instant in the MPC optimization problem. The proposed algorithm is characterized by a computational burden similar to the one required by stabilizing MPC methods for deterministic systems, by the possibility to consider unbounded noises, and by guaranteed recursive feasibility and convergence.