A Frequency Domain Perspective on Nonlinear System Identification: Methods, Models, and Modern Advances

Nonlinear system identification remains a fundamental yet challenging task in control engineering, particularly when applying frequency-domain methods that were traditionally designed for linear systems. This review provides a comprehensive analysis of recent advancements in frequency-domain approaches for the identification of nonlinear systems. While classical techniques excel in linear modeling, extending them to nonlinear dynamics introduces significant complexity due to nonlinearity, noise characteristics, and model structure ambiguity. The paper categorizes state-of-the-art methods, including frequency sweep techniques, variational inference, Student’s t-distribution models, and coevolutionary algorithms. It also highlights the role of hybrid approaches that integrate signal processing and machine learning to enhance model accuracy and adaptability. Through critical analysis of recent literature and case studies, this review identifies prevailing trends, technical limitations, and potential research gaps. The findings aim to inform the development of more robust and efficient identification frameworks for complex nonlinear systems.