Stochastic linear Model Predictive Control with chance constraints – A review

In the past ten years many Stochastic Model Predictive Control (SMPC) algorithms have been developed for systems subject to stochastic disturbances and model uncertainties. These methods are motivated by many application fields where a-priori knowledge of the stochastic distribution of the uncertainties is available, some degree of constraint violation is allowed, and nominal operation should be defined as close as possible to the operational constraints for economic/optimality reasons. However, despite the large number of methods nowadays available, a general framework has not been proposed yet to classify the available alternatives. For these reasons, in this paper the main ideas underlying SMPC are first presented and different classifications of the available methods are proposed in terms of the dynamic characteristics of the system under control, the performance index to be minimized, the meaning and management of the probabilistic (chance) constraints adopted, and their feasibility and convergence properties. Focus is placed on methods developed for linear systems. In the first part of the paper, all these issues are considered, also with the help of a simple worked example. Then, in the second part, four algorithms representative of the most popular approaches to SMPC are briefly described and their main characteristics are discussed.