Machine Learning (ML) and linear System Identification (SI) have been historically developed independently. In this paper, we leverage well-established ML tools - especially the automatic differentiation framework - to introduce SIMBa, a family of discrete linear multi-step-ahead state-space SI methods using backpropagation. SIMBa relies on a novel Linear-Matrix-Inequality-based free parametrization of Schur matrices to ensure the stability of the identified model. We show how SIMBa generally outperforms traditional linear state-space SI methods, and sometimes significantly, although at the price of a higher computational burden. This performance gap is particularly remarkable compared to other SI methods with stability guarantees, where the gain is frequently above 25% in our investigations, hinting at SIMBa's ability to simultaneously achieve state-of-the-art fitting performance and enforce stability. Interestingly, these observations hold for a wide variety of input-output systems and on both simulated and real-world data, showcasing the flexibility of the proposed approach. We postulate that this new SI paradigm presents a great extension potential to identify structured nonlinear models from data, and we hence open-source SIMBa on https://github.com/Cemempamoi/simba.

翻译：机器学习与线性系统辨识在历史上独立发展。本文利用成熟的机器学习工具——特别是自动微分框架——提出SIMBa，一类基于反向传播的离散线性多步前向状态空间系统辨识方法。SIMBa采用一种新颖的基于线性矩阵不等式的舒尔矩阵自由参数化方法，以确保所辨识模型的稳定性。研究表明，尽管计算负担较高，但SIMBa在整体上优于传统线性状态空间系统辨识方法，部分情况下优势显著。与其他具有稳定性保证的系统辨识方法相比，这一性能差距尤为突出——在我们的研究中增益常超过25%，暗示SIMBa能够同时实现最先进的拟合性能与稳定性保证。有趣的是，这些观测结果适用于多样化的输入-输出系统，且在仿真与真实数据上均成立，展示了所提方法的灵活性。我们推测，这一新型系统辨识范式在从数据中辨识结构化非线性模型方面具有巨大拓展潜力，并将SIMBa在https://github.com/Cemempamoi/simba上开源。