Make a Loose -Callback Equipment System Recognition Based on the Koopman Operator

This study proposes a data-driven method for nonlinear system identification by leveraging the Koopman operator theory to embed nonlinear dynamical systems into a high-dimensional space, enabling linear evolution of the system dynamics within that space. In the absence of control inputs, this method is equivalent to numerically approximating the associated Koopman operator. Furthermore, we apply the Koopman operator to controlled dynamical systems and compute finite-dimensional approximations of the operator via the extended dynamic mode decomposition (EDMD), yielding a form analogous to linear controlled dynamical systems. Numerical examples validate the efficacy of the proposed method. The system identification process is entirely data-driven, involving only nonlinear transformations of data and solving a linear least-squares problem in the lifted space, enabling effective handling of large datasets from industrial production. In the application to a surge tank system, we consider the input-output mapping under full-state measurement and incorporate actual production disturbances, with the identified model performing well on the test dataset.