Sparse least squares via fractional function group fractional function penalty for the identification of nonlinear dynamical systems

This work proposes a method called fractional function group fractional function penalty sparse least squares to identify nonlinear dynamical systems. It integrates least squares with fractional function group fractional function penalty with the aim to enhance sparsity and accuracy of regression tasks. Additionally, we develop an optimization algorithm called the threshold fractional function group fractional function penalty sparse least squares. The choice of threshold parameters throughout the algorithm is accomplished by employing the L-curve criterion. The simulation experiments involving two ordinary differential equations and one partial differential equation illustrate that our proposed method has superior identification performance especially on larger noisy state measurements compared to existing methods, signifying that our new method is effective across a wide variety of latent applications.