This article develops an identification algorithm for nonlinear systems. Specifically, the nonlinear system identification problem is formulated as a sparse recovery problem of a homogeneous variant searching for the sparsest vector in the null subspace. An augmented Lagrangian function is utilized to relax the nonconvex optimization. Thereafter, an algorithm based on the alternating direction method and a regularization technique is proposed to solve the sparse recovery problem. The convergence of the proposed algorithm can be guaranteed through theoretical analysis. Moreover, by the proposed sparse identification method, redundant terms in nonlinear functional forms are removed and the computational efficiency is thus substantially enhanced. Numerical simulations are presented to verify the effectiveness and superiority of the present algorithm.

中文翻译：

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使用稀疏零子空间方法的数据驱动发现面向块的非线性模型


本文开发了一种非线性系统的识别算法。具体来说，非线性系统辨识问题被表述为在零子空间中搜索最稀疏向量的齐次变体的稀疏恢复问题。利用增广拉格朗日函数来放松非凸优化。此后，提出了一种基于交替方向法和正则化技术的算法来解决稀疏恢复问题。通过理论分析可以保证所提算法的收敛性。此外，通过所提出的稀疏识别方法，去除了非线性函数形式中的冗余项，从而大大提高了计算效率。数值模拟验证了该算法的有效性和优越性。