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

arXiv: https://arxiv.org/abs/2602.12047 · HTML: https://mlsanity.com/paper/2602.12047/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Adaptive Conformal Prediction for Motion Planning among Dynamic Agents](https://mlsanity.com/paper/2212.00278/) (2022)
- [Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processes](https://mlsanity.com/paper/1603.04915/) (2016)
- [Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constants](https://mlsanity.com/paper/2010.08993/) (2020)
- [Multi-Agent Reachability Calibration with Conformal Prediction](https://mlsanity.com/paper/2304.00432/) (2023)
- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Fighting Uncertainty with Gradients: Offline Reinforcement Learning via Diffusion Score Matching](https://mlsanity.com/paper/2306.14079/) (2023)
- [Learning for CasADi: Data-driven Models in Numerical Optimization](https://mlsanity.com/paper/2312.05873/) (2023)
- [Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems](https://mlsanity.com/paper/2104.08695/) (2021)
- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systems](https://mlsanity.com/paper/2212.06874/) (2022)
- [Robust Tracking with Model Mismatch for Fast and Safe Planning: an SOS Optimization Approach](https://mlsanity.com/paper/1808.00649/) (2018)
- [Robust Nonlinear Optimal Control via System Level Synthesis](https://mlsanity.com/paper/2301.04943/) (2023)
- [Robust Model Predictive Control with Polytopic Model Uncertainty through System Level Synthesis](https://mlsanity.com/paper/2203.11375/) (2022)
- [Quantifying Aleatoric and Epistemic Dynamics Uncertainty via Local Conformal Calibration](https://mlsanity.com/paper/2409.08249/) (2024)
- [Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions](https://mlsanity.com/paper/2401.13762/) (2024)
- [Robustly Constrained Dynamic Games for Uncertain Nonlinear Dynamics](https://mlsanity.com/paper/2509.16826/) (2025)
- [Safe, Out-of-Distribution-Adaptive MPC with Conformalized Neural Network Ensembles](https://mlsanity.com/paper/2406.02436/) (2024)
- [Guaranteed Robust Nonlinear MPC via Disturbance Feedback](https://mlsanity.com/paper/2509.18760/) (2025)
- [Stochastic MPC with Online-optimized Policies and Closed-loop Guarantees](https://mlsanity.com/paper/2502.06469/) (2025)
- [Data-Driven System Level Synthesis](https://mlsanity.com/paper/2011.10674/) (2020)
- [Improving Out-of-Distribution Generalization of Learned Dynamics by Learning Pseudometrics and Constraint Manifolds](https://mlsanity.com/paper/2403.12245/) (2024)
- [Probabilistically-Safe Bipedal Navigation over Uncertain Terrain via Conformal Prediction and Contraction Analysis](https://mlsanity.com/paper/2510.07725/) (2025)

## Built on by (most cited first, 7 of 7)

- [Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control](https://mlsanity.com/paper/2604.19018/) (2026)
- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)
- [Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPC](https://mlsanity.com/paper/2606.15594/) (2026)
- [VISION-SLS: Safe Perception-Based Control from Learned Visual Representations via System Level Synthesis](https://mlsanity.com/paper/2604.24894/) (2026)
- [Robustness without Wrinkles: Parallel Simulation and Robust MPC for Certified Deformable Manipulation](https://mlsanity.com/paper/2606.14188/) (2026)
- [Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllers](https://mlsanity.com/paper/2605.25346/) (2026)
- [GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics](https://mlsanity.com/paper/2607.01203/) (2026)

## Abstract (arXiv)

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.