2022/05/30 by Moad Abudia, Abudia, Moad, Joel A. Rosenfeld +3 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Control Systems and Identification #FOS: Electrical engineering #Model Reduction and Neural Networks #Neural Networks and Applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2205.15009
openalex publication_date 2022/05/30 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28
This paper concerns identification of uncontrolled or closed loop nonlinear systems using a set of trajectories that are generated by the system in a domain of attraction. The objective is to ensure that the trajectories of the identified systems are close to the trajectories of the real system, as quantified by an error bound that is prescribed a priori. A majority of existing methods for nonlinear system identification rely on techniques such as neural networks, autoregressive moving averages, and spectral decomposition that do not provide systematic approaches to meet pre-defined error bounds. The developed method is based on Carleman linearization-based lifting of the nonlinear system to an infinite dimensional linear system. The linear system is then truncated to a suitable order, computed based on the prescribed error bound, and parameters of the truncated linear system are estimated from data. The effectiveness of the technique is demonstrated by identifying an approximation of the Van der Pol oscillator from data within a prescribed error bound.