Application of fuzzy logic controls on hyperbolic differential equations
Year: 2025
Type: article
Abstract: The selection of suitable fuzzy logic control (FLC) systems for stabilizing hyperbolic conservation laws (HCLs) remains an open issue in computational fluid dynamics (CFD), particularly for shock-capturing schemes. This work addresses this gap by adopting a dual methodological strategy: (i) a systematic review of over 50 studies (2000–2025) on flux-limiting FLC approaches, and (ii) a comparative benchmark of Mamdani- and Sugeno-type FLCs applied to discontinuous solutions of HCLs. Our results demonstrate that, using weighted average defuzzification, Sugeno-type systems achieve approximately a 20% reduction in mean square error compared to the Mamdani centroid-based method in shock-dominated regimes. This performance gain aligns with adaptive CFD practices that prioritize rule-based, computationally inexpensive smoothing. By integrating theoretical analysis with experimental validation, this work strengthens the mathematical foundations of fuzzy control in PDE-driven modeling.
Authors: Ruchika Lochab, Luckshay Batra
Institutions: International Management Institute, Amity University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,470
OpenAlex ID: W4413758516