Abstract
We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers distribution-free probabilistic bounds on the state tracking error under Koopman modeling uncertainty. Conformal prediction is employed here to rigorously derive a bound on the state-dependent modeling uncertainty throughout the trajectory, ensuring safety and robustness without assuming a specific error prediction structure or distribution. Unlike prior approaches that merely combine conformal prediction with Koopman-based control in an open-loop setting, our method establishes a closed-loop control architecture with formal guarantees that explicitly account for both forward and inverse modeling errors. Also, by expressing the tracking error bound in terms of the control parameters and the modeling errors, our framework offers a quantitative means to formally enhance the performance of arbitrary Koopman-based control. We validate our method both in numerical simulations with the Dubins car and in real-world experiments with a highly nonlinear flapping-wing drone. The results demonstrate that our method indeed provides formal safety guarantees while maintaining accurate tracking performance under Koopman modeling uncertainty.
Abstract (translated)
本文提出了一种完全数据驱动、基于Koopman算子的框架，用于对具有线性嵌入的离散时间非线性系统进行统计鲁棒控制。通过建立Koopman算子与收缩理论之间的联系，该框架在Koopman建模不确定性下提供了分布无关的状态跟踪误差概率边界。本文采用共形预测方法，严格推导了沿轨迹的状态相关建模误差边界，无需假设特定的误差预测结构或分布即可确保安全性与鲁棒性。与以往仅以开环方式结合共形预测与基于Koopman的控制方法不同，本文方法建立了具有形式化保证的闭环控制架构，明确考虑了前向与逆建模误差。此外，通过将跟踪误差边界表示为控制参数与建模误差的函数，本框架为定量提升任意基于Koopman的控制性能提供了形式化手段。我们在杜宾斯车模型的数值仿真以及高度非线性的扑翼无人机实物实验中验证了该方法。结果表明，在Koopman建模不确定性下，本文方法确实能提供形式化安全保证，同时保持精确的跟踪性能。
URL
https://arxiv.org/abs/2603.21580
