A new model of Hopfield network with fractional-order neurons for parameter estimation

In this work, we study an application of fractional-order Hopfield neural networks for optimization problem solving. The proposed network was simulated using a semi-analytical method based on Adomian decomposition,, and it was applied to the on-line estimation of time-varying parameters of nonlinear dynamical systems. Through simulations, it was demonstrated how fractional-order neurons influence the convergence of the Hopfield network, improving the performance of the parameter identification process if compared with integer-order implementations. Two different approaches for computing fractional derivatives were considered and compared as a function of the fractional-order of the derivatives: the Caputo and the Caputo-Fabrizio definitions. Simulation results related to different benchmarks commonly adopted in the literature are reported to demonstrate the suitability of the proposed architecture in the field of on-line parameter estimation.

Automated summary

This work explores the application of fractional-order Hopfield neural networks in solving optimization problems and online parameter estimation for nonlinear dynamical systems. The study shows how fractional-order neurons impact the convergence of the Hopfield network, improving parameter identification performance compared to integer-order implementations. By considering and comparing different methods for computing fractional derivatives, the Caputo and Caputo-Fabrizio definitions were evaluated based on simulation results with various benchmarks, demonstrating the effectiveness of the proposed architecture for online parameter estimation.