Online Optimal Input Excitation Signal for Sparse Identification of Euler-Lagrangian Systems

This paper addresses the limitations of the Sparse Identification of Nonlinear Dynamical Systems (SINDy) methods, which, while effective in identifying system dynamics with minimal prior knowledge, often depend on stochastic input excitation, which limits performance. To overcome this, we propose an Online-Optimal xL-SINDy (OOL-SINDy) framework that generates optimal excitation signals for sparse identification of Euler-Lagrange systems. The framework employs a one-step-ahead optimization strategy based on D-optimality criteria, enhancing information richness during system identification, thereby improving the convergence rate. Simulation on pendulum models show superior performance of the proposed method compared to stochastic inputs, while respecting system constraints.