Recursive Sparse Identification of Nonlinear Dynamics for Online Equation Discovery

The dynamic model equations are essential in system analysis and control system design. In adaptive control systems, the mathematical equations of the controlled system are utilized to compute the corresponding control signals based on the current dynamic conditions of the system. The challenge intensifies when dealing with nonlinear systems, as the equation discovery process becomes more intricate. This paper proposes the Recursive Sparse Identification of Nonlinear Dynamics (R-SINDy) using Least Square-Assisted LASSO (Least Absolute Shrinkage and Selection Operator), an extension of the previous SINDy method that processed data in batches for online equation discovery. This method aims to generate mathematical equations for both linear and nonlinear dynamic systems in online streaming data. The proposed method is tested on two nonlinear systems: Lorenz Chaotic System with parameter changes and dataset of KUKA robotic manipulator. The results indicate that the proposed method has the ability to quickly adjust the gain when changes occur because of the adjustment in the forgetting factor, achieving an accuracy of up to 100 % on the Lorenz system and 92.02 % on the robotic manipulator, with a sparsity coefficient of up to 87.59 % from a total of 282 available matrix coefficients.