Modeling and parameter estimation for fractional large‐scale interconnected Hammerstein systems

Abstract This paper addresses the challenge of modeling and identifying large‐scale interconnected systems exhibiting memory effects, hereditary properties, and non‐local interactions. We propose a fractional‐order extension of the Hammerstein architecture that incorporates Grünwald–Letnikov operators to capture complex dynamics through multiple fractional differentiation orders ( ). The framework features cross‐subsystem coupling via fractional differencing and polynomial nonlinearities operating on fractionally filtered signals. For parameter estimation, we develop a fractional recursive extended least squares (FRELS) algorithm with rigorous convergence guarantees established through fractional stochastic approximation theory. Numerical validation demonstrates significant improvements in modeling accuracy, including reduced steady‐state errors and superior tracking of time‐varying parameters compared with classical integer‐order approaches. The framework provides enhanced capabilities for systems exhibiting long‐range dependence, anomalous diffusion, and frequency‐dependent coupling phenomena.