Stochastic MPC for Finite Gaussian Mixture Disturbances with Guarantees

Abstract: This paper presents a stochastic model predictive control (SMPC) algorithm for linear systems subject to additive Gaussian mixture disturbances, with the goal of satisfying chance constraints. We focus on a special case where each Gaussian mixture component has a similar variance. To solve the SMPC problem, we formulate a branch model predictive control (BMPC) problem on simplified dynamics and leverage stochastic simulation relations (SSR). Our contribution is an extension of the SMPC literature to accommodate Gaussian mixture disturbances while retaining recursive feasibility and closed-loop guarantees. We illustrate the retention of guarantees with a case study of vehicle control on an ill-maintained road.