System identification based on sparse approximation of Koopman operator

A data-driven system identification method based on the Koopman operator with sparse optimization is proposed. Koopman theory provides insights into transforming nonlinear systems into a higher-dimensional measurement function space dominated by a linear Koopman operator, which enhances system identification. The effective data-driven approach of the eigenfunctions of the Koopman operator is becoming a challenging topic. Compared with the state-of-the-art methods, this paper introduces a sparse basis selection algorithm to enhance the implementation of the compressed Koopman operator. The validity and accuracy of the method are demonstrated in a 2D Duffing system and a 3D chaotic Lorenz system. The method is also robust to noisy data.