FUZZY FRACTIONAL CONTINUOUS HOPFIELD NETWORKS BASED ON THE GRÜNWALD–LETNIKOV FORMULATION FOR OPTIMAL ECONOMIC DISPATCH PROBLEMS

Abstract

 Continuous Hopfield Networks (CHNs) have long served as efficient neurodynamic solvers for constrained optimization problems due to their parallel computing and convergence capabilities. However, their reliance on fixed weight and bias parameters limits adaptability in dynamic and uncertain environments. To overcome these limitations, we propose a novel Fuz-Frac-CHN Fractional CHN model that integrates fractional-order calculus with a fuzzy logic system to dynamically tune Grunwald–Letnikov (GL) coefficients based on real-time system feedback.
The proposed method is applied to the Economic Dispatch (ED) problem I power systems, aiming to minimize generation costs while satisfying power balance and generator constraints. Extensive simulations show that the Fuz-Frac-CHN model achieves superior performance in convergence speed, solution feasibility, and robustness compared to both classical CHN and fixed-order fractional CHN models. In particular, it maintains negligible power mismatch (on the order of MW) while achieving competitive cost outcomes across varying fractional orders. The adaptive tuning of GL memory weights enables the network to self-regulate learning dynamics, improving optimization under different operating conditions. Beyond the ED case, the proposed framework demonstrates potential for generalization to a wide range of constrained optimization problems in control systems, intelligent networks, and industrial engineering. The integration of fuzzy rules with memory-aware neural computation offers a scalable, flexible, and intelligent optimization paradigm that bridges the gap between neurodynamics, fractional calculus, and soft computing.