Identifying the Dynamics of a System by Leveraging Data from Similar Systems
Identifying the Dynamics of a System by Leveraging Data from Similar Systems
复制标题
通过利用类似系统的数据来识别系统的动态
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
S. Sundaram
中科院分区：
文献类型：
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作者：
Lei Xin;Lintao Ye;G. Chiu;S. Sundaram
除了来自真实系统的数据之外，当人们可以访问由类似（但不相同）系统生成的样本时，我们研究识别线性系统动力学的问题。我们使用加权最小二乘法，并为已识别动态的质量提供有限样本性能保证。我们的结果表明，可以有效地利用相似系统生成的辅助数据来减少由于过程噪声而导致的估计误差，但代价是增加一部分由于真实系统和辅助系统模型的内在差异而导致的误差。我们还提供数值实验来验证我们的理论结果。我们的分析可以应用于各种重要的设置。例如，如果系统动态在某个时间点发生变化（例如，由于故障），那么应该如何利用先前系统的数据来了解新系统的动态？另一个例子，如果从真实系统的模拟（但不完美）模型中可以获得大量数据，那么与系统中的真实数据相比，应该如何对该数据进行加权？我们的分析提供了对这些问题答案的见解。
We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and provide finite sample performance guarantees on the quality of the identified dynamics. Our results show that one can effectively use the auxiliary data generated by the similar system to reduce the estimation error due to the process noise, at the cost of adding a portion of error that is due to intrinsic differences in the models of the true and auxiliary systems. We also provide numerical experiments to validate our theoretical results. Our analysis can be applied to a variety of important settings. For example, if the system dynamics change at some point in time (e.g., due to a fault), how should one leverage data from the prior system in order to learn the dynamics of the new system? As another example, if there is abundant data available from a simulated (but imperfect) model of the true system, how should one weight that data compared to the real data from the system? Our analysis provides insights into the answers to these questions.