Robustifying Model Predictive Control of Uncertain Linear Systems with Chance Constraints

TL;DR

This paper introduces a robust model predictive control method for uncertain linear systems with stochastic disturbances, ensuring chance constraint satisfaction through probabilistic invariant sets, while maintaining computational simplicity.

Contribution

It develops a novel approach to guarantee chance constraints in MPC for linear systems with stochastic disturbances using probabilistic invariant sets, with a straightforward quadratic programming formulation.

Findings

Guarantees chance constraint satisfaction under stochastic disturbances.

Maintains recursive feasibility and stability in the control scheme.

Demonstrates effectiveness through a numerical example.

Abstract

This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set for constraint tightening with the help of the computation of the minimal robust positively invariant set, the chance constraints are guaranteed, assuming only the mean and covariance of the disturbance distribution are given. The resulting online optimization problem is a standard strictly quadratic programming, just like in conventional model predictive control with recursive feasibility and stability guarantees and is simple to implement. A numerical example is provided to illustrate the proposed method.