Safety Beyond the Training Data: Robust Out-of-Distribution MPC via Conformalized System Level Synthesis

TL;DR

This paper introduces a new approach combining conformal prediction and system level synthesis to enhance safety and robustness in model predictive control for systems operating outside their training data distribution.

Contribution

It develops a framework that provides high-confidence error bounds and integrates them into a robust MPC formulation, ensuring safety beyond training data.

Findings

Improves safety and robustness in nonlinear systems like cars and quadcopters.

Provides theoretical guarantees on coverage and robustness under distributional drift.

Demonstrates effectiveness on complex systems outside training data distribution.

Abstract

We present a novel framework for robust out-of-distribution planning and control using conformal prediction (CP) and system level synthesis (SLS), addressing the challenge of ensuring safety and robustness when using learned dynamics models beyond the training data distribution. We first derive high-confidence model error bounds using weighted CP with a learned, state-control-dependent covariance model. These bounds are integrated into an SLS-based robust nonlinear model predictive control (MPC) formulation, which performs constraint tightening over the prediction horizon via volume-optimized forward reachable sets. We provide theoretical guarantees on coverage and robustness under distributional drift, and analyze the impact of data density and trajectory tube size on prediction coverage. Empirically, we demonstrate our method on nonlinear systems of increasing complexity, including a 4D car and a {12D} quadcopter, improving safety and robustness compared to fixed-bound and non-robust baselines, especially outside of the data distribution.