Modeling and Prediction of Nonlinear Dynamic System Models by Deep Neural Networks and Koopman-Based Subspace Identification

Abstract

Traditional methods for modelling nonlinear dynamic systems often suffer from high computational complexity and limited prediction accuracy. To address these challenges, this paper proposes a novel Koopman operator-based framework that integrates deep neural networks with subspace identification. The core idea of the framework is to decouple the overall modeling task by assigning distinct roles to its components: the deep neural network is dedicated to learning the nonlinear lifting map, while subspace identification handles the linear dynamic evolution in the lifted space. This approach improves computational efficiency while preserving model interpretability. Comparative experiments on both weakly nonlinear and strongly nonlinear systems show that the proposed method achieves high modeling accuracy with significantly reduced errors. Further theoretical stability analysis and validation under parameter perturbations confirm the reliability of the proposed approach, offering an effective and robust solution for nonlinear system modeling.