Identification of Nonlinear Dynamical Systems: When Deep Koopman Operator Meets Incremental Gaussian Process Regression

This article proposes a deep Koopman-based identification method for nonlinear dynamical systems with modeling residuals learned recursively by incremental Gaussian process regression (IGPR). This method introduces encoder and decoder networks within the Koopman framework, enabling linear identification of a nonlinear system through a lifted state-space representation that yields an approximately globally linear model. Furthermore, an IGPR model is introduced to compensate for modeling residuals in an online form, effectively reducing multistep estimation errors and enhancing identification adaptivity under varying disturbances or operating conditions. Finally, research studies on the numerical example, several public benchmark datasets, and the aeroengine platforms are performed to verify the efficacy of the developed approach.