## 5 Conclusions  
This paper presents an online approach for tuning weighting factors in the finite control set model predictive current control of permanent magnet synchronous motor drive systems. The proposed method effectively tackles the challenge of designing weighting factors for asymmetric cost functions to achieve a balance among multiple control objectives inherent in traditional model predictive current control. By using a TD3-based deep reinforcement learning agent to choose the weighting factors online, we enable real-time tuning across various operating conditions and multiple objectives, ensuring optimal control performance. The method is specifically designed to optimize weighting factors for multi-objective system performance, allowing for efficient real-time adjustments to meet dynamic operational requirements. Comparative validation test results confirm the effectiveness of the proposed approach in determining optimal weighting factors for the asymmetric cost function.  
Furthermore, the proposed TD3-based algorithm, by allowing online optimization of the weighting factors in an asymmetric cost function, effectively adapts to varying operating conditions without requiring manual tuning. However, due to the lack of a general theoretical framework to ensure the stability of RL algorithms, extensive validation remains essential prior to industrial deployment. The proposed DRL-based control strategy represents a significant step forward in intelligently addressing multiple conflicting objectives within the model predictive control framework. By learning to dynamically tune the weighting factors, the algorithm improves both steady-state and transient performance, demonstrated through reduced torque ripple, lower current harmonics, and smoother switching transitions. This intelligent weighting approach allows the control system to balance performance trade-offs more effectively than static or manually tuned approaches. The proposed design is capable of incorporating multiple additional objectives, such as voltage constraints and efficiency optimization, which will be key directions in future work.  
Figure 14: Total harmonic distortion under a load of 5 Nm and shaft speed of 300 rpm.  
This enables the development of a more adaptive control strategy capable of maintaining optimal performance across a wide range of operating conditions.  
Conceptualization, M.U.; methodology, M.U.; validation, M.U.; writing--original draft preparation, M.U. and A.S.; writing--review and editing, M.U., A.S., T.C. and N.L.; supervision, T.C. and N.L.; funding acquisition, N.L. All authors have read and agreed to the submitted version of the manuscript.  
This work was supported by ANR and Region Normandie through the HAISCoDe (ANR-20-THIA-0021) and PAMAP projects.  
Not applicable.  
The datasets used and/or analyzed during the current study are available from the corresponding author upon request.  
The authors declare no competing interests.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} ANN & Artificial neural network \\ CCS & Continuous control set \\ DDPG & Deep deterministic policy gradient \\ DRL & Deep reinforcement learning \\ FCS & Finite control set \\ IAE & Integral absolute error \\ ISE & Integral squared error \\ ITAE & Integral time-weighted absolute error \\ ITSE & Integral time-weighted squared error \\ MOGA & Multi-objective genetic algorithm \\ MDP & Markov decision process \\ MPC & Model predictive control \\ MPCC & Model predictive current control \\ NN & Neural network \\ PI & Proportional-integral \\ PMSM & Permanent magnet synchronous motor \\ RL & Reinforcement learning \\ SAC & Soft Actor Critic \\ SMPC & Sequential model predictive control \\ SPMSM & Surface permanent magnet synchronous motor \\ TD3 & Twin Delayed Deep Deterministic Gradient \\ THD & Total harmonic distortion \\ VSI & Voltage source inverter \\ \end{tabular}