无需假设不确定性的模型，用数据驱动方法保证非线性系统控制的稳定性。
Conformal Contraction for Robust Nonlinear Control with Distribution-Free Uncertainty Quantification
- 基于收缩理论与数据预测结合，不依赖不确定性模型
- 通过置信预测实现有限时间、分布无关的概率保障
- 适合对鲁棒性要求高且不确定性强的控制系统设计
我们提出一种针对连续时间扰动非线性动力系统的新型鲁棒控制框架，其不确定性同时依赖于状态和控制输入。与传统方法不同，该框架不施加不确定性结构假设，而是将数据驱动的不确定性预测融入收缩型鲁棒控制，对不确定性及预测器模型保持无感。通过共形预测，统计量化了在存在不确定性时收缩条件被满足的可靠性，从而获得轨迹跟踪误差指数有界的分布自由、有限时间概率保证。进一步提出概率鲁棒控制不变（PRCI）管，用于分布鲁棒运动规划，在该管内，扰动系统轨迹以有限概率被保证不超出，且无需显式知道不确定性模型。数值仿真验证了所提鲁棒控制框架的有效性及PRCI管的性能。
原文摘要 · Abstract (English)
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.
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