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

We present a novel framework for robust out-of-distribution planning and control using conformal prediction (CP) and system level synthesis (SLS). Our method addresses the challenge of ensuring safety and robustness when using learned dynamics models beyond the training data distribution. We first derive high-confidence bounds on model errors using weighted conformal prediction with a learned, state-control-dependent covariance model. These bounds are then integrated into an SLS-based robust nonlinear model predictive control (RMPC) 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 approach on nonlinear systems of increasing complexity, including a 4D car and a {12D} quadcopter, showing improved safety and reliability compared to fixed-bound and non-robust baselines, especially outside of the collected data distribution.