标题： 无分布不确定性量化的鲁棒非线性控制的共形收缩 显示英文标题

标题： Conformal Contraction for Robust Nonlinear Control with Distribution-Free Uncertainty Quantification

摘要： 我们提出了一种新的鲁棒控制框架，用于具有不确定性的连续时间非线性动力系统，该不确定性非线性地依赖于状态和控制输入。 与传统方法对不确定性的结构假设不同，我们的框架通过数据驱动的不确定性预测增强了基于收缩的鲁棒控制，对不确定性和预测器的模型保持无知。 我们通过共形预测统计量化了在存在不确定性的动态下收缩条件被满足的可靠性，从而获得了轨迹跟踪误差指数有界性的分布无关且有限时间的概率保证。 我们进一步提出了概率鲁棒控制不变（PRCI）管，用于分布鲁棒运动规划，在该管内，受扰系统轨迹以有限概率被保证不偏离，而无需明确了解不确定性的模型。 数值仿真验证了所提出的鲁棒控制框架的有效性以及PRCI管的性能。 显示英文摘要

摘要： We present a novel robust control framework for continuous-time, perturbed nonlinear dynamical systems with uncertainty that depends nonlinearly on both the state and control inputs. Unlike conventional approaches that impose structural assumptions on the uncertainty, our framework enhances contraction-based robust control with data-driven uncertainty prediction, remaining agnostic to the models of the uncertainty and predictor. We statistically quantify how reliably the contraction conditions are satisfied under dynamics with uncertainty via conformal prediction, thereby obtaining a distribution-free and finite-time probabilistic guarantee for exponential boundedness of the trajectory tracking error. We further propose the probabilistically robust control invariant (PRCI) tube for distributionally robust motion planning, within which the perturbed system trajectories are guaranteed to stay with a finite probability, without explicit knowledge of the uncertainty model. Numerical simulations validate the effectiveness of the proposed robust control framework and the performance of the PRCI tube.