One of the main theoretical challenges in learning dynamical systems from data is providing upper bounds on the generalization error, that is, the difference between the expected prediction error and the empirical prediction error measured on some finite sample. In machine learning, a popular class of such bounds are the so-called Probably Approximately Correct (PAC) bounds. In this paper, we derive a PAC bound for stable continuous-time linear parameter-varying (LPV) systems. Our bound depends on the H2 norm of the chosen class of the LPV systems, but does not depend on the time interval for which the signals are considered.

翻译：从数据中学习动态系统的主要理论挑战之一是为泛化误差提供上界，即期望预测误差与在有限样本上测量的经验预测误差之间的差异。在机器学习中，一类常用的此类界是所谓概率近似正确（PAC）界。本文推导了稳定连续时间线性参数变化（LPV）系统的PAC界。该界依赖于所选LPV系统类别的H2范数，但不依赖于信号所考虑的时间区间。