非线性动力系统的数据驱动Koopman行为距离

中文摘要 AI 辅助

直接从轨迹数据比较非线性动力系统仍然具有挑战性，因为有限时域轨迹表示通常依赖于坐标。受近期针对线性系统的行为子空间方法的启发，本文提出了一种利用多轨迹展开数据的非线性随机系统的Koopman行为距离。状态测量通过一个共同的观测字典进行提升，并在不显式识别Koopman算子的情况下，使用Grassmannian距离比较主导的提升行为子空间。我们建立了坐标不变性、在精确提升闭包下与近期提出的线性行为距离的联系，以及对近似闭包的鲁棒性。数值示例展示了坐标不变性和参数判别能力。

英文摘要

Comparing nonlinear dynamical systems directly from trajectory data remains challenging because finite-horizon trajectory representations are generally coordinate dependent. Motivated by recent behavioral subspace approaches for linear systems, this paper introduces a Koopman-behavioral distance for nonlinear stochastic systems using multi-rollout trajectory data. State measurements are lifted through a common observable dictionary, and dominant lifted behavioral subspaces are compared using Grassmannian distances without explicit Koopman operator identification. We establish coordinate invariance, connection with recently proposed linear behavioral distances under exact lifted closure, and robustness to approximate closure. Numerical examples demonstrate coordinate invariance and parameter discrimination.

发表机构

• Clemson University（克莱姆森大学）

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