## 1 Introduction  
Permanent magnet synchronous motors (PMSM) are widely used in industrial applications due to their high precision, high efficiency, and excellent control performance. However, PMSM drive systems typically exhibit inherent nonlinearities and variable coupling characteristics, making conventional linear control strategies, such as PI controllers, inadequate to guarantee optimal operational performance. To overcome these nonlinear control challenges, advanced methods including fuzzy logic control, robust control, sliding-mode control, and finite control set model predictive control (FCS-MPC) have been proposed and thoroughly investigated. In particular, FCS-MPC methods enable multivariable optimization, rapid dynamic responses, and flexible handling of system constraints, which are highly suitable to power electronics applications [1, 2]. The basic principle of an MPC algorithm is to predict the system's future outputs corresponding to different inverter voltages. Subsequently, the strategy selects the optimal switching state by minimizing a defined cost function. Although, in theory, FCS-MPC provides superior performance without requiring complex modulation strategies, it is inherently sensitive to parameter uncertainties due to its predictive structure. Specifically, the predictive model relies significantly on accurate system parameters, making parameter accuracy crucial for optimal inverter voltage selection. In practical PMSM systems, critical electromagnetic parameters (such as stator resistance, dq-axis inductances, and flux linkage) experience inevitable fluctuations resulting from magnetic saturation effects and thermal drift, as well as harmonic distortions [3; 4; 5]. These parameter deviations lead to accumulated prediction errors, consequently degrading overall system control accuracy and causing increased torque ripple, speed oscillations, and efficiency deterioration [6]. To address these challenges, several solutions have been actively explored in prior research. One promising method to enhance the robustness of predictive controllers is to avoid direct dependence on machine parameters, which is known as model-free predictive control. The model-free prediction achieves robustness by directly predicting currents without explicitly relying on PMSM parameters [7; 8; 9]. However, this approach typically introduces greater sensitivity to measurement noise, particularly under high frequency switching conditions. As an alternative, online parameter identification schemes have demonstrated effectiveness in compensating for parameter variations and improving prediction accuracy [10; 11; 12; 13]. Notable implementations include least-squares estimation for L-type converters, virtual flux-based inductance adaptation, and recursive algorithms for LCL-filter identification. Despite their proven effectiveness, these parameter estimation strategies often incur considerable computational burden due to algorithm complexity, significantly constraining their suitability for practical, real-time control applications [14]. Recent studies have explored integrating artificial neural networks (ANNs) with FCS-MPC to alleviate its intrinsic limitations [15; 16; 17; 18; 19; 20; 21]. For instance, ANN-based implementations have been proposed for real-time adjustment of weighting factors in power converter FCS-MPC schemes [16; 17]. These methods effectively address the critical design challenge of balancing reference tracking and switching frequency objectives. Furthermore, experimental validations conducted on DC-DC converters and three-phase inverter systems further confirmed that hybrid ANN-MPC approaches can achieve reduced total harmonic distortion (THD) and superior dynamic response characteristics [18; 19]. Additionally, research presented in [20] demonstrated that entirely replacing the traditional MPC structure with an ANN can significantly simplify the computational burden while maintaining comparable or even enhanced performance.