###### Abstract  
Proton exchange membrane fuel cells (PEMFC) are considered a promising solution for renewable energy application. To meet industrial requirements, the power source consisting of PEMFC is required to be power regulator to generate a stable and desired current and/or voltage under various working conditions. In this article, the adaptive sliding mode control integrating with the radial basis function neural network (RBFNN) approach for DC/DC buck converter-based PEMFC is presented to address perturbations from inner parameters as well as external disturbances in terms of power conditioning. Sliding mode control (SMC) and backstepping schemes are integrated to tackle the nonlinear and coupled outputs resulting in large control errors and slow response caused by PEMFC characteristics. To accurately estimate the parametric uncertainties and disturbance injections, such as buck converter parameter varying and PEMFC operation point changing, the RBFNN adaptive law is developed according to the defined Lyapunov and Gaussian functions overcoming the limitations of non-/linear parameter estimating. Simulations and experiments on the PEMFC power supply prototype governed by the DS1104 board are carried out. The comparative results indicate that the proposed RBFNN estimation associated with the backstepping SMC can reduce up to 7.5% overshoot and smooth PEMFC voltage and inductor current when disturbance changes in a voltage regulation experiment. Thus, the proposed method can regulate the current or voltage of a PEMFC power supply with robustness, adaptivity, and no chattering phenomenon. t 14 December 202  
and external load demands can also be changed that result in uncertainties as well as disturbances. Robust control approaches such as linear matrix inequalities (LMI) combined with a Takagi-Sugeno (T-S) fuzzy controller [12] and a structured singular value-based \(\mu\)-method [13] were proposed to solve the robustness when uncertainty and disturbance were taken into consideration. To apply optimal control schemes to achieve performance index minimization with robust stability, a linear matrix inequalities and linear-quadratic regulator (LMI-LQR) control was introduced, where a convex optimization problem was finally transformed [14]. Similarly, the piecewise-affine (PWA) equations were introduced to solve the constrained model predictive control (MPC) [15; 16], in which [PERSON] et al. [15] determined that disturbances in the buck converter input voltage were effectively rejected, and [PERSON] et al. [16] focused on a fast MPC by constructing a sparse QP problem for the linear parameter-varying (LPV) system of a buck converter in a low CPU runtime. Moreover, a disturbance estimator for observing the disturbance caused by load changes [17] and real-time parameter estimation based on the Kalman filter [18] were presented to improve the tracking performance under the buck converter working condition of disturbance and model parameter perturbation. A variable structure control based on the sliding mode control (SMC) has been considered as a powerful method for regulating DC/DC converters. SMC exhibits many benefits when applied in DC/DC converters such as a wide range stability, robustness against parameter vibrations, and fast dynamic response. However, oscillations of the state tracking around the sliding manifold may cause a chattering phenomenon. [PERSON] et al. [19] proposed a second-order sliding-mode (SOSM) to achieve output voltage tracking problems in the presence of model uncertainties and external disturbances, and the results showed that SOSM had a faster dynamic response and smaller chattering phenomenon compared with first-order SMC. Aiming at the smooth output of the boost-buck converter used in PEMFC systems under perturbations and load disturbances, the high-order sliding mode controller (HOSM) was developed in [20]. To eliminate the chattering phenomenon, the backstepping scheme can be used in combination with SMC.