Conformal Prediction-Based MPC for Stochastic Linear Systems

TL;DR

This paper introduces a conformal prediction-based stochastic MPC framework for linear systems that guarantees chance constraint satisfaction with minimal offline computation, even under unknown disturbance distributions.

Contribution

It develops a novel MPC approach using conformal prediction to create confidence regions, relaxing chance constraints into deterministic ones, applicable to output feedback with guarantees.

Findings

Effective in satisfying joint-in-time chance constraints.

Reduces offline computational requirements compared to existing methods.

Demonstrates advantages through numerical examples.

Abstract

We propose a stochastic model predictive control (MPC) framework for linear systems subject to joint-in-time chance constraints under unknown disturbance distributions. Unlike existing approaches that rely on parametric or Gaussian assumptions, or require expensive offline computation, the method uses conformal prediction to construct finite-sample confidence regions for the system's error trajectories with minimal computational effort. These probabilistic sets enable relaxation of the joint-in-time chance constraints into a deterministic closed-loop formulation based on indirect feedback, ensuring recursive feasibility and chance constraint satisfaction. Further, we extend to the output feedback setting and establish analogous guarantees from output measurements alone, given access to noise samples. Numerical examples demonstrate the effectiveness and advantages compared to existing approaches.