Stochastic MPC for Finite Gaussian Mixture Disturbances with Guarantees

TL;DR

This paper develops a stochastic model predictive control method for linear systems affected by Gaussian mixture disturbances, ensuring chance constraint satisfaction and recursive feasibility, with practical validation in vehicle control scenarios.

Contribution

It extends SMPC to handle Gaussian mixture disturbances while maintaining recursive feasibility and guarantees, using stochastic simulation relations.

Findings

Successfully applied to vehicle control on rough roads.

Retains recursive feasibility under Gaussian mixture disturbances.

Provides closed-loop guarantees with the proposed approach.

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.