Stochastic MPC with Offline Uncertainty Sampling

TL;DR

This paper introduces an offline sampling-based stochastic model predictive control method for linear systems with parametric uncertainty, improving computational efficiency and robustness guarantees over traditional online scenario approaches.

Contribution

It proposes a novel offline sampling approach for stochastic MPC, providing theoretical bounds and enabling faster online computation with guaranteed constraint satisfaction.

Findings

Significantly reduces online computation time

Provides rigorous bounds on sample size for chance constraints

Ensures robust recursive feasibility and stability

Abstract

For discrete-time linear systems subject to parametric uncertainty described by random variables, we develop a sampling-based Stochastic Model Predictive Control algorithm. Unlike earlier results employing a scenario approximation, we propose an offline sampling approach in the design phase instead of online scenario generation. The paper highlights the structural difference between online and offline sampling and provides rigorous bounds on the number of samples needed to guarantee chance constraint satisfaction. The approach does not only significantly speed up the online computation, but furthermore allows to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided. Under mild assumptions, asymptotic stability of the origin can be established.