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.

翻译：我们提出了一种新颖的鲁棒分布外规划与控制框架，该方法结合保形预测与系统级综合技术，旨在解决学习动力学模型在超出训练数据分布时确保安全性与鲁棒性的挑战。我们首先利用带权重的保形预测方法，结合学习得到的状态-控制相关协方差模型，推导出高置信度的模型误差界。这些误差界被整合到基于系统级综合的鲁棒非线性模型预测控制框架中，该框架通过体积优化的前向可达集在预测时域内执行约束紧缩。我们为分布漂移情况下的覆盖度与鲁棒性提供了理论保证，并分析了数据密度与轨迹管尺寸对预测覆盖度的影响。在实证研究中，我们在复杂度递增的非线性系统（包括4自由度车辆模型与12自由度四旋翼系统）上验证了所提方法。实验表明，相较于固定误差界与非鲁棒基线方法，本方法显著提升了安全性及鲁棒性，尤其在数据分布外区域表现更为突出。