Discovering State-Space Representation of Dynamical Systems From Noisy Data

In this paper, we introduce a systematic methodology to discover state-space representations of dynamical systems from noisy data. Our approach utilizes a fusion of basis functions to adeptly estimate both the structure and parameters inherent in the systems under investigation. To strengthen the robustness of our methodology, we integrate estimation algorithms grounded in both deterministic and stochastic approaches. Through extensive simulations, we showcase the efficacy of our proposed method in accurately uncovering the state-space representations of diverse dynamical systems. The synergy of versatile basis functions and advanced estimation algorithms enhances our approach to navigate the complexity inherent in various systems, offering a reliable and accurate framework for the discovery of equations from empirical data. The results highlight the potential of the proposed method as a versatile tool for system identification, capable of providing accurate insights into the underlying dynamics of complex systems based on observed data.