Fast Stochastic MPC using Affine Disturbance Feedback Gains Learned Offline

TL;DR

This paper introduces a fast stochastic MPC method that uses offline learning to simplify online optimization, achieving similar control performance with significantly reduced computational time.

Contribution

It presents a novel offline learning approach to extract features of disturbance feedback policies, enabling efficient online stochastic MPC for uncertain linear systems.

Findings

Achieves 10-fold reduction in computational time compared to classical methods.

Maintains comparable control performance and Region of Attraction.

Uses data-driven sampling to approximate chance-constrained feasible sets.

Abstract

We propose a novel Stochastic Model Predictive Control (MPC) for uncertain linear systems subject to probabilistic constraints. The proposed approach leverages offline learning to extract key features of affine disturbance feedback policies, significantly reducing the computational burden of online optimization. Specifically, we employ offline data-driven sampling to learn feature components of feedback gains and approximate the chance-constrained feasible set with a specified confidence level. By utilizing this learned information, the online MPC problem is simplified to optimization over nominal inputs and a reduced set of learned feedback gains, ensuring computational efficiency. In a numerical example, the proposed MPC approach achieves comparable control performance in terms of Region of Attraction (ROA) and average closed-loop costs to classical MPC optimizing over disturbance feedback policies, while delivering a 10-fold improvement in computational speed.