Structured Koopman Lifted Finite Memory Identification via Truncated Grunwald Letnikov Kernels
The framework combines Koopman lifting with a truncated Grunwald–Letnikov memory term to model nonlinear systems with finite history dependence. It achieves this by rewriting the non-Markovian recursion into a linear regression problem, allowing identification of the lifted model from data. This method provides an exact augmented Markovian realization and quantifies the error introduced by approximating infinite memory with a finite kernel.