Stochastic MPC of Systems with Additive Disturbance using Scenario Optimization*

In this paper a stochastic model predictive control (SMPC) scheme for linear systems with additive disturbance is presented. The goal is to design a controller that minimizes the expected value of an objective function while guaranteeing mean-square exponential input-tostate stability (MSE-ISS) and constraints on the states and inputs. The SMPC is partitioned into an offline computation based on a bilinear matrix inequality (BMI) problem for ensuring ISS, constraint satisfaction, and recursive feasibility and an online optimization based on a quadratically constrained quadratic programming (QCQP) problem for including knowledge about the additive disturbance while relaxing ISS to MSE-ISS. The partition into an offliine computation and online optimization allows addressing stability, feasibility, and performance separately and therefore improving performance as well as handling disturbances which may not be independent identically distributed (i.i.d.). The effectiveness of the SMPC scheme is evaluated by simulations and assessed by comparison with a robust MPC scheme.