Data-Driven Koopman Based System Identification for Partially Observed Dynamical Systems with Input and Disturbance

The identification of dynamical systems from data is essential in control theory, enabling the creation of mathematical models that accurately represent the behavior of complex systems. However, real-world applications often present challenges such as the unknown dimensionality of the system and limited access to measurements, particularly in partially observed systems. The Hankel alternative view of Koopman (HAVOK) method offers a data-driven approach to identify linear representations of nonlinear systems, but it often overlooks the influence of external control signals (inputs) and disturbances. This paper introduces a novel input-aware modeling method for unstable linear systems using data-driven Koopman analysis. By explicitly incorporating the impact of inputs and disturbances, our method enhances the accuracy and robustness of system identification, even in the face of incomplete observations. The proposed approach leverages Koopman operator theory on augmented state-input data to capture both the intrinsic dynamics and the system’s sensitivity to external control. Through extensive numerical examples, we demonstrate the effectiveness of our method in accurately identifying and predicting the behavior of various dynamical systems, including real-world nonlinear systems and simulated unstable linear systems with and without disturbances. The results highlight the potential of our approach to advance the field of system identification and control, offering a powerful tool for modeling and analyzing complex systems in diverse applications.