In this paper, we propose an approach for identifying linear and nonlinear discrete-time state-space models, possibly under $\ell_1$- and group-Lasso regularization, based on the L-BFGS-B algorithm. For the identification of linear models, we show that, compared to classical linear subspace methods, the approach often provides better results, is much more general in terms of the loss and regularization terms used, and is also more stable from a numerical point of view. The proposed method not only enriches the existing set of linear system identification tools but can be also applied to identifying a very broad class of parametric nonlinear state-space models, including recurrent neural networks. We illustrate the approach on synthetic and experimental datasets and apply it to solve the challenging industrial robot benchmark for nonlinear multi-input/multi-output system identification proposed by Weigand et al. (2022). A Python implementation of the proposed identification method is available in the package \texttt{jax-sysid}, available at \url{https://github.com/bemporad/jax-sysid}.

翻译：本文提出一种基于L-BFGS-B算法的方法，用于在线性与非线性离散时间状态空间模型辨识中（可能采用ℓ₁与组Lasso正则化）。在辨识线性模型时，我们证明该方法相比经典线性子空间方法，通常能提供更优结果，在损失函数与正则化项的使用上更具通用性，同时从数值角度更稳定。该方法不仅丰富了现有线性系统辨识工具集，还可应用于辨识包含循环神经网络在内的极宽泛参数化非线性状态空间模型。我们通过合成数据集与实验数据集验证该方法，并将其应用于解决Weigand等人(2022)提出的工业机器人非线性多输入/多输出系统辨识基准挑战。所提辨识方法的Python实现已收录于\texttt{jax-sysid}软件包（下载地址：\url{https://github.com/bemporad/jax-sysid})。