###### Abstract
The advantage of the backstepping scheme is that it divides the system into several linear subsystems, and each is easily controlled. Backstepping methods have been widely used in the DC/DC converter control. A backstepping-based control was proposed to solve the robust problems of unmodeled nonlinearities and dynamics of a boost converter [21]. [PERSON] et al. [22] presented a backstepping method for two-level voltage source converter trajectory planning. An indirect backstepping approach was introduced to regulate the output voltage for flyback-type DC/DC converters [23]. To track the maximum power point of a photovoltaic system, [PERSON] et al. [24] designed a backstepping SMC. In addition, the adaptive control can handle system uncertainties, such as parameters varying and being mismatched, as well as external disturbances. Estimations of system perturbations including variations of capacitance, inductance and load resistance [25; 26; 27; 28], and the inductor current observation [27] were developed according to adaptive backstepping techniques to improve the robustness. PEMFC outputs nonlinear stack voltages under the different working currents, temperatures, and pressures of reactants [1; 2; 3; 4; 5; 28]. Additionally, in the combined PEMFC-fed buck converter, the input voltage of the converter supplied by PEMFC is coupled with a load current that may result in the energy conversion system operation point varying when the load is changing. Neural network control is a competitive method of addressing the nonlinear and coupled features of the control plant; it has outstanding advantages in extracting and learning knowledge and strong control robustness. [PERSON] et al. [29] presented a control scheme with back propagation (BP) neural network for the buck circuit and realized the idea of introducing neural network into DC/DC converter control, and the simulation results showed that under the condition of rapid fluctuation of input voltage and load, the controller had good dynamic response characteristics. The BP network is a global approximation network. Each time the network learns, it needs to iteratively update the weights of all layers, which leads to a slow training speed. At the same time, the BP algorithm often causes many local minimal points, which makes the algorithm unable to guarantee the convergence to the optimal solution. [PERSON] et al. [30] proposed a radial basis function neural network (RBFNN) control scheme with good dynamic and static performance to tuning proportion integration differentiation (PID) control in an improved bidirectional DC/DC converter. Neural network disturbance observer has diversity, such as RBF, Elman neural network [31], fuzzy neural network [32], and Hermite neural network [33]. In particular, the RBF network is a local approximation network with the advantage of avoiding the local minimum problem. The linear mapping of the RBF neural network (RBFNN) from the hidden layer to the output layer is the only parameter that needs to be adjusted during the learning process of the RBFNN; because this linear relationship ensures that the error surface is quadratic, it is easy to find the minimum value and greatly improve the learning speed. In addition, the RBFNN can perform partial weight modification without parameter iteration; therefore, the RBFNN is selected for regulating the abovementioned PEMFC-fed power supply in this study. Unmanned aerial vehicle (UAV) modeling and attitude controls via robust neural network estimation were reported in [34; 35]. Moreover, in the hybrid energy system [36] and the motor-driven control [37], neural networks showed the superiority of the tracking performance against disturbances. A series of the DC/DC buck converter adaptive control by using neural network estimator are presented in [38; 39; 40], and the results indicated a fast and accurate response with the disturbance rejection ability.