## 1 Introduction
### Literature Review
In the presence of uncertainties and disturbances, the application of adaptive barrier function-based gain for unit control has effectively achieved an arbitrary a priori predefined uniform ultimate bound for solutions [21]. [PERSON] proposes a bi-powered extension of the methodology, which can effectively adjust the size of the final set for any value of the upper bound of the perturbation [22]. [PERSON] proposed a novel adaptive sliding mode control design that effectively obtained a robust sliding mode adaptive-gain control law under the assumption of boundness system characteristics [23]. [PERSON] utilized a low-pass filter to evaluate the so-called equivalent control, effectively reducing the high-frequency oscillations associated with sliding mode control. This approach helps mitigate the chattering phenomenon, which is common in sliding mode control systems, enhancing both stability and performance in practical implementations [24]. In disturbed linear systems, the use of robust nonlinear model reference adaptive control strategies effectively improves the algorithm's execution speed. This control approach enhances system response times by quickly adapting to disturbances and uncertainties, offering robust performance under dynamic conditions [25]. Adaptive high-order sliding mode control has become a hot topic in recent years, as it effectively addresses unknown bounds while mitigating chattering. This control strategy enhances system performance by improving robustness and stability under uncertainties, making it suitable for various applications [26]. The speed and torque overshoot of PMSMs are critical factors in evaluating control strategies for these motors. Optimizing control strategies using appropriate optimization algorithms is particularly significant in this regard [27; 28]. MOPSO and NSGA II are popular multi-objective optimization algorithms that have successfully addressed various multi-objective optimization problems across numerous fields. Their effectiveness in providing optimal solutions has made them widely adopted in applications such as engineering design, logistics, and resource management [29; 30]. [PERSON] proposed a three-stage, seven-step optimization method assisted by neural networks. This method employs neural network techniques to provide dedicated correction factors for analyzing PMSM quality and loss estimates across the design space, resulting in faster and more accurate auxiliary analysis models [31]. [PERSON] applied [PERSON]'s Hoo Observer-Kalman Filter Optimization algorithm for parameter estimation in PMSMs, with simulation experiments demonstrating its superior convergence rate and error performance evaluation [32]. [PERSON] introduced the Chaotic Whale Optimization Variant optimization technique, with overall results indicating that the CwoA-II variant, utilizing logistic chaotic mapping, exhibits the best performance among all variants. It shows smaller error values between estimation and original system performance, faster convergence, and shorter execution time, ensuring rapid motor control and protection against damage [33]. [PERSON] presented a multi-objective optimization design for PMSMs based on the Multi-Objective Comprehensive Teaching and Learning Algorithm. This approach addresses the complexity of PMSM optimization problems and the presence of numerous variables. The algorithm, an improvement over teaching and learning-based optimization algorithms, demonstrates better adaptation to large-scale sample spaces and multivariate optimization [34]. [PERSON] proposed a new voltage optimization algorithm to enhance the operating performance of PMSMs. This algorithm, based on the particle swarm algorithm, combines online and secondary optimization improvements. The results show a 16.22% reduction in current ripple and a 65.14% decrease in steady-state speed fluctuation compared to a similar speed response achieved with Dual Vector Modulated Predictive Current Control [35].