## 1 Introduction  
The integration of renewable energies, such as solar and wind power, into the electrical grid is revolutionizing the traditional paradigm of electricity generation. Unlike conventional thermal, nuclear, or hydraulic power plants that rely on electrical machines, renewable energy systems primarily use power electronic converters to interface with the grid. Among these, DC-DC converters, particularly boost converters, are crucial for stepping up voltage levels to meet grid requirements [1; 2]. Traditionally, these converters have used Proportional-Integral controllers (PI) controllers [3]. However, Model Predictive Control (MPC) is now recognized as a superior strategy due to its ability to handle fast dynamic behaviors in modern power converters. MPC predicts future system states and optimizes control inputs in real time, ensuring a rapid response to changes in operating conditions. This predictive capability allows MPC to manage various performance criteria, such as voltage regulation, current control, and efficiency optimization, simultaneously through a single cost function [4; 5; 6]. MPC is implemented in two main forms: Continuous Control Set (CCS) and Finite Control Set (FCS). CCS-MPC operates on a continuous range of control inputs, providing smooth control but requiring high computational power and complex algorithms, making it less suitable for fast dynamics and real-time applications [7; 8]. In contrast, FCS-MPC uses a discrete set of control actions, significantly reducing computational demands and enabling quicker decision making [9; 10]. However, FCS-MPC faces challenges, such as stability issues when the sampling step is relatively big and the difficulty of managing non-minimum phase behavior in systems like boost converters when the prediction horizon is short [11]. To address the non-minimum phase issue in boost converters, a long-horizon approach is presented by [PERSON] et al. [12] that employs machine learning for the adaptive prediction horizon in FCS-MPC, but the method's complexity can be a disadvantage in real-time applications. Among short-horizon solutions, [PERSON] et al. [13] propose an input-state linearization method for FCS-MPC, transforming system dynamics to eliminate instability with a short prediction horizon. Another method presented by [PERSON] et al. [14] designs a specific cost function within the FCS-MPC framework for stable and precise voltage tracking, minimizing the output voltage error and smoothing control actions. Similarly, [PERSON] et al. [15] address the issue in active front end rectifiers with a predictive control strategy based on output power and DC link capacitor energy, avoiding additional modulators and achieving a zero steady-state error. [PERSON] et al. [16] present a DMPCC strategy for DC-DC boost converters using a hybrid model for precise current regulation, reducing computational complexity. [PERSON] et al. [17] use a non-linear MPC method with a partially saturating ferrite core inductor model to manage magnetic saturation and losses, ensuring correct voltage regulation. All these methods require precise parameter estimation, with inaccuracies leading to suboptimal performance, and are affected by load and input condition variations, necessitating robust estimation and adjustment mechanisms. Another approach is to control the inductor current with an FCS-MPC controller, where the reference for the controller is provided by a PI controller [18; 19; 20]. In this method, the PI controller generates the reference current for the FCS-MPC based on the output voltage error. While this hybrid approach aims to combine the strengths of both controllers--using the PI controller for steady-state accuracy and the FCS-MPC for handling fast dynamics--the overall speed is compromised. The PI controller's slower response time can negate the advantage of the FCS-MPC's rapid switching capability, potentially missing out on the primary benefit of using an FCS-MPC.