Identification of hybrid dynamic systems via a sparse regression algorithm

This study introduces a sparse regression algorithm for identifying hybrid dynamical systems and the intricate switching dynamics between force fields. Using a physics-informed approach and assuming the number of discontinuities is known, the algorithm employs a coordinate transformation to explicitly reveal switching surfaces. A symbolic representation of the dynamics is recovered using sparse regularized regression. Our approach is numerically validated on a system with unilateral elastic impacts. We investigate the capabilities and limitations of the method, particularly with respect to impact strength, which defines a low-data regime for observables and limited contact information. The practical applicability is evaluated using an experimental rig featuring a two-well potential chaotic oscillator with an impact barrier. We demonstrate the robustness and versatility of the approach in recovering hybrid dynamic models from complex scenarios involving both smooth and non-smooth transitions between force fields. By combining physics-informed insights with symbolic regression techniques, this method enhances interpretability and robustness in the analysis of hybrid dynamical systems.