###### Abstract
Reference [23] introduced a deep learning-based hybrid dynamic modeling approach that combines data-driven techniques with classical dynamic equations to enhance accuracy in modeling vehicle behavior under these conditions. Their study demonstrates the effectiveness of the hybrid model in improving prediction accuracy, especially in edge cases like rapid acceleration, sharp turns, or slippery surfaces. longitudinal collision avoidance and lateral stability adaptive control system based on MPC of autonomous vehicles [24], in this work they have proposed a model predictive control (MPC)-based adaptive control system designed for autonomous vehicles (AVs), with a dual focus on longitudinal collision avoidance and lateral stability. The research addresses critical safety and control challenges to enhance AV reliability during complex driving scenarios. A particularly challenging scenario for longitudinal control systems in autonomous vehicles is driving on downhill roads. Maintaining consistent speed and stability in such conditions requires precise coordination of throttle and braking mechanisms, as the gravitational force increases vehicle acceleration. Downhill driving poses additional challenges such as an increased risk of brake overheating and reduced traction, especially on steep gradients or slippery surfaces [1,3]. Advanced vehicle control strategies, including model predictive control (MPC), parameter estimation, and uncertainty compensation, have been investigated to tackle autonomous vehicle challenges [25, 26, 27]. These methods focus on optimizing distribution, minimizing external disturbances, and accurately estimating key parameters to ensure robust performance under varying road conditions. Parameter estimation plays a vital role in real-time adaptation, allowing the control system to dynamically adjust braking force and throttle inputs based on environmental and vehicle-specific factors. Gradient-aware control algorithms and parameter estimation techniques have proven effective in improving speed regulation during downhill motion [28; 29]. Furthermore, incorporating real-time road slope prediction and adaptive braking systems can significantly enhance the safety and energy efficiency of autonomous vehicles in such environments [30]. This underscores the importance of developing advanced control algorithms, equipped with reliable parameter estimation capabilities, tailored to challenging driving scenarios like downhill roads, which remain a critical area of research in autonomous driving. Thus, previous studies have proposed control algorithms to enhance system performance. However, most of these papers fail to consider the impact of non-linear road scenarios, relying instead on conventional controllers, such as PID, which often lead to suboptimal performance. Additionally, many of the proposed controllers lack robustness, making them highly sensitive to uncertainties and external disturbances, particularly in challenging conditions like downhill roads. This paper proposes a high-performance controller known as optimized super-twisting sliding mode control (OST-SMC), designed to overcome the shortcomings of prior works. The primary contribution of this research is the incorporation of a linear regression approach, specifically gradient descent, for estimating the uncertain parameters of the proposed controller. Furthermore, the controller compensates for disturbances from the downhill roads through a continuous and non-linear design, mitigates the chattering problem inherent in traditional sliding mode controllers, and achieves robustness under non-linear scenarios. This paper also provides a comprehensive finite-time stability analysis based on Lyapunov theory and presents experimental implementations in MATLAB/Simulink and CarMaker, encompassing various driving conditions, including downhill and straight roads.