Sparse identification of dynamical systems by reweighted l₁-regularized least absolute deviation regression

This work proposes a generalized methodology for sparse identification of dynamical systems (SID), utilizing reweighted l₁-regularized least absolute deviation (LAD) regression to recover the governing equation of dynamical systems. To programmatically implement the proposed method, a stabilized and efficient resolution scheme is developed by combining the solution method of the classical LAD-based least absolute shrinkage and selection operator (LAD-lasso) and the threshold iterative idea of the sequentially thresholded least-squares (STLS) method. The new method relaxes the assumption of normality for the error terms in the linear regression model employed by traditional SID techniques. Additionally, it overcomes the low identification accuracy deficiency of the recently proposed regularized least absolute deviation-based sparse identification of dynamics method (RLAD-SID) under some poor data conditions. The performance of the proposed approach is investigated by simulations of two well-known dynamical systems, that is, the Lorenz system and the Duffing system. The reliability of this approach in recovering the governing equation of dynamical systems from noise-contaminated datasets is firstly demonstrated. Furthermore, the advantage of the proposed method is illustrated by comparing it with four traditional techniques in relatively poor data environments. Finally, we display the robustness of the new method when the time derivative dataset is affected by different types of noise, and reveal its superiority compared to the traditional RLAD-SID.