Sparse identification of nonlinear dynamical systems via non-convex penalty least squares

This paper proposes a non-convex penalty regression method to identify governing equations of nonlinear dynamical systems from noisy state measurements. The idea to connect the non-convex penalty function instead of the l₁ - norm with least squares is due to the fact that the l₁ - norm excessively penalizes large coefficients and may incur estimation bias. The purpose of this work is to improve the accuracy and robustness in regression tasks. A threshold non-convex penalty sparse least squares optimization algorithm is developed, wherein the threshold parameter is selected using the L-curve criterion. With two examples of nonlinear dynamical systems, we illustrate the accuracy and robustness of the non-convex penalty least squares on noisy state measurements, indicating the validity of our method in a wide range of potential applications.