Deep Dictionary-Free Method for Identifying Linear Model of Nonlinear System with Input Delay
Modeling nonlinear systems with input delays remains challenging due to the failure of conventional linear methods and the difficulty of constructing appropriate basis function dictionaries. To address this, we propose an LSTM-enhanced, dictionary-free deep Koopman framework. Our method eliminates reliance on predefined basis dictionaries by leveraging LSTM networks to automatically learn latent temporal dependencies between past inputs and states, thereby enabling linear approximation of nonlinear dynamics in a learned embedding space. Crucially, input delays are implicitly encoded within the Koopman operator learning process, obviating explicit delay feature engineering. Experimental results demonstrate that our approach achieves significantly higher prediction accuracy than extended dynamic mode decomposition (eDMD) on unknown nonlinear systems, while matching eDMD’s performance on systems with known dynamics—indicating strong generalization capability and robustness.