A Data-Integrated Framework for Learning Fractional-Order Nonlinear Dynamical Systems
This addresses modeling complex systems with memory effects for researchers in dynamical systems and control, though it appears incremental as it builds on existing fractional-order concepts with a new algorithmic framework.
The paper tackles learning dynamics of fractional-order nonlinear systems by proposing a data-integrated framework that estimates fractional order and reconstructs vector fields using orthonormal basis functions. Results show the framework accurately learns dynamics in four benchmark systems, with fractional-order models outperforming integer-order ones in capturing long-range dependencies.
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step, input-output experiments are designed to generate the necessary datasets for learning the system dynamics, including the fractional order, the drift vector field, and the control vector field. In the second step, these datasets, along with the memory-dependent property of fractional-order systems, are used to estimate the system's fractional order. The drift and control vector fields are then reconstructed using orthonormal basis functions. To validate the proposed approach, the algorithm is applied to four benchmark fractional-order systems. The results confirm the effectiveness of the proposed framework in learning the system dynamics accurately. Finally, the same datasets are used to learn equivalent integer-order models. The numerical comparisons demonstrate that fractional-order models better capture long-range dependencies, highlighting the limitations of integer-order representations.