We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide a finite sample error bound of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.

翻译：我们考虑在获取真实系统数据之外，还可获取由具有相似（但非相同）动态特性的辅助系统生成的数据时，学习线性系统动态的问题。我们采用加权最小二乘法，并给出了学习模型在有限样本下的误差界，该误差界是样本数量、两系统的各类参数以及赋予辅助数据的权重的函数。研究表明：辅助数据有助于降低由噪声引起的固有系统辨识误差，但代价是引入了因两系统模型差异产生的误差分量。我们进一步给出了在具备部分系统先验知识时可计算的数据依赖误差界，该误差界还可用于确定模型训练阶段应赋予辅助数据的权重值。