Fractional-Order Swarming Intelligence Heuristics for Nonlinear Sliding-Mode Control System Design in Fuel Cell Hybrid Electric Vehicles

Due to climate change, the electric vehicle (EV) industry is rapidly growing and drawing researchers interest. Driving conditions like mountainous roads, slick surfaces, and rough terrains illuminate the vehicles inherent nonlinearities. Under such scenarios, the behavior of power sources (fuel cell, battery, and super-capacitor), power processing units (converters), and power consuming units (traction motors) deviates from nominal operation. The increasing demand for FCHEVs necessitates control systems capable of handling nonlinear dynamics, while ensuring robust, precise energy distribution among fuel cells, batteries, and super-capacitors. This paper presents a DSMC strategy enhanced with Robust Uniform Exact Differentiators for FCHEV energy management. To optimally tune DSMC parameters, reduce chattering, and address the limitations of conventional methods, a hybrid metaheuristic framework is proposed. This framework integrates moth flame optimization (MFO) with the gravitational search algorithm (GSA) and Fractal Heritage Evolution, implemented through three spiral-based variants: MFOGSAPSO-A (Archimedean), MFOGSAPSO-H (Hyperbolic), and MFOGSAPSO-L (Logarithmic). Control laws are optimized using the Integral of Time-weighted Absolute Error (ITAE) criterion. Among the variants, MFOGSAPSO-L shows the best overall performance with the lowest ITAE for the fuel cell (56.38), battery (57.48), super-capacitor (62.83), and DC bus voltage (4741.60). MFOGSAPSO-A offers the most accurate transient response with minimum RMSE and MAE FC (0.005712, 0.000602), battery (0.004879, 0.000488), SC (0.002145, 0.000623), DC voltage (0.232815, 0.058991), and speed (0.030990, 0.010998)—outperforming MFOGSAPSO, GSA, and PSO. MFOGSAPSO-L further reduces the ITAE for fuel cell tracking by up to 29% over GSA and improves control smoothness. PSO performs moderately but lags under transient conditions. Simulation results conducted under EUDC validate the effectiveness of the MFOGSAPSO-based DSMC framework, confirming its superior tracking, faster convergence, and stable voltage control under transients making it a robust and high-performance solution for FCHEV.