A Comparative Study of Stochastic Model Predictive Controllers

Abstract

A comparative study of two state-of-the-art stochastic model predictive controllers for linear systems with parametric and additive uncertainties is presented. On the one hand, Stochastic Model Predictive Control (SMPC) is based on analytical methods and solves an optimal control problem (OCP) similar to a classic Model Predictive Control (MPC) with constraints. SMPC defines probabilistic constraints on the states, which are transformed into equivalent deterministic ones. On the other hand, Scenario-based Model Predictive Control (SCMPC) solves an OCP for a specified number of random realizations of uncertainties, also called scenarios. In this paper, Classic MPC, SMPC and SCMPC are compared through two numerical examples. Thanks to several Monte-Carlo simulations, performances of classic MPC, SMPC and SCMPC are compared using several criteria, such as number of successful runs, number of times the constraints are violated, integral absolute error and computational cost. Moreover, a Stochastic Model Predictive Control Toolbox was developed by the authors, available on MATLAB Central, in which it is possible to simulate a SMPC or a SCMPC to control multivariable linear systems with additive disturbances. This software was used to carry out part of the simulations of the numerical examples in this article and it can be used for results reproduction.