IEEE Trans Cybern. 2022 May;52(5):3794-3804. doi: 10.1109/TCYB.2020.3015705. Epub 2022 May 19.
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.
本文提出了一种非线性系统的辨识算法。具体来说，将非线性系统辨识问题表述为齐次变分搜索法的稀疏恢复问题，即寻找零空间中最稀疏的向量。利用增广拉格朗日函数来松弛非凸优化问题。然后，提出了一种基于交替方向法和正则化技术的算法来求解稀疏恢复问题。通过理论分析可以保证所提出算法的收敛性。此外，通过所提出的稀疏辨识方法，可以去除非线性函数形式中的冗余项，从而大大提高计算效率。通过数值模拟验证了所提出算法的有效性和优越性。
