## 1 Introduction  
The issue of environmental pollution has been receiving great attention from governments and people around the world in recent decades [1, 2]. One of the culprits for this problem comes from the carbon dioxide emission of vehicles that use fossil fuels, such as gasoline or diesel, to generate energy [3]. Meanwhile, the shortage of fossil fuels leads to the requirement of employing alternative sustainable energy resources, such as fuel cells (FCs), solar energy, wind energy, and so on, in industrial applications instead of using the above traditional fuels. Among them, solar and wind energy resources have some disadvantages of severe weather dependence, expensive storage systems, and large installation space, as well as being associated with pollution. Hence, although the cost of hydrogen production is now relatively high, fuel cell energy still is considered a potential power source for future power systems due to its high power production and zero-emissions, as well as the qualities of reliability, high efficiency, and compactness [4, 5]. However, some disadvantages of the fuel cell systems such as low-and-unregulated output voltage and excessive ripples of output current [6] restrain their applicability in real-life applications. In order to amplify the output voltage of FC energy systems and maintain a constant DC bus voltage at a high-level stable voltage, DC-DC boost converters or step-up converters [7, 8, 9] are generally adopted as an interface between the low-voltage side (FC) and high-voltage side (DC bus). Conventional DC-DC boost converters have the benefits of low-cost and simple structure; however, their voltage gains are relatively small due to the parasitic resistance on the inductors and capacitors [10]. Hence, numerous enhanced topologies of DC-DC step-up converters [4; 6; 11; 12; 13; 14; 15; 16] have been innovated and they are demonstrated to be more appropriate for fuel cell applications than the conventional boost converter. As an illustration of them, interleaved boost converters (IBCs) [13; 17; 18; 19; 20] can be considered a remarkable selection with their high amplifying coefficient and low voltage stress for power switches. In addition, by virtue of interleaved structure, IBCs are tolerant towards a low input current ripple, and consequently, they are suitable for a wide range of FC-based applications. However, how to achieve a desired voltage regulation qualification for such IBCs in the presence of input variation and load change is still a challenging task that has attracted considerable attention from the research community recently. It should be noted that the proportional-integral-derivative (PID) controllers and their modifications are still valuable solutions for regulating the output voltage of step-up DC-DC converters, which were broadly employed in previous works [21; 22; 23; 24; 25]. For instance, [PERSON] et al. [21] developed a combination between a new switch strategy and a fractional order PID controller for a four-switch buck-boost converter, whose controller gains were optimized using a partial swarm optimization (PSO) algorithm, and consequently, a better performance was achieved compared to the conventional integer order controller. In addition, in [22], [PERSON] and [PERSON] constructed a voltage regulation loop in which a disturbance observer-based proportional-derivative (DOB-based PD) controller for DC-DC boost converters was established to maintain a constant output voltage and cope with the parameter and load variations, simultaneously. In addition, a robust PID controller using the equivalent feedforward of the modified direct synthesis (MDS) approach, which incorporates the dynamic disturbance model in the controller design phase [23] for DC-DC boost converters, was constructed. To increase the voltage regulation performance and the robustness of the closed-loop system, various robust nonlinear control techniques have been adopted.