###### Abstract  
Longitudinal motion control is a critical aspect of autonomous vehicle area, requiring a well-designed controller to ensure optimal system performance, safety, and comfort under varying driving conditions. Previous control methods often face challenges such as chattering effects, and model uncertainties. To address such challenges, in this paper, we propose the application of an optimized super-twisting sliding mode control (OST-SMC) for the longitudinal motion control of autonomous vehicles. The motivation is to enhance the robustness and efficiency of the control system while minimizing the chattering problem. The proposed system's mathematical modeling and control design are presented in detail with stability analyzed using Lyapunov theory. To enhance the controller's performance, uncertain parameters are optimized using the gradient descent method, a linear regression-based technique. The OST-SMC algorithm shows enhanced robustness against disturbances and parameter uncertainties compared to conventional sliding mode controllers. Simulations in MATLAB/Simulink and CarMaker validate the proposed method, demonstrating strong performance even on downhill roads. The OST-SMC reduces chattering more effectively than traditional SMCs, achieving smooth tracking and consistent robustness under varying road conditions. autonomous vehicle; downhill road; longitudinal motion control; parameter estimation; super-twisting sliding mode control; Lyapunov theory 2020 ac  
during long-distance travel. By relieving drivers from the physical effort of maintaining pedal pressure and the mental effort of monitoring speed to avoid speeding tickets, cruise control systems help reduce both physical and cognitive fatigue during highway driving. A basic cruise control system allows the driver to set a speed reference using a simple push-button interface [6,7]. The longitudinal control system, such as cruise control, is designed to maintain the vehicle's speed set by the user and ensure that the system consistently achieves the desired output. This can be achieved by various methods of the controller such as using proportional-integral derivatives (PID) controller, fuzzy logic controller, and many more [8]. SMC has been widely applied to nonlinear systems, multi-input multi-output (MIMO) systems, discrete-time models, large-scale and infinite-dimension systems, and stochastic systems. The most eminent feature of SMC and its type is that it is completely insensitive to parametric uncertainty and external disturbances during sliding mode but suffers from chattering phenomena on its control input [9, 10, 11]. Many researchers have been working on longitudinal control systems, the following papers are some of them. In [1], the authors have designed a conventional PI as upper controller for cruise controller system, a PID controller design for cruise control system using a genetic algorithm [6], a cruise control system with feedforward controller for all-terrain vehicles [12], a cruise control design using fuzzy logic controller [13], an optimal PID controller for an automobile cruise control system [14], an optimized robust cruise control system for an electric vehicle [15], a cruise control for electric vehicle based on ADRC controller considering driver's behavior [16], a cruise control based on gain scheduling PI diesel engine speed controller [17], a historical review on lateral and longitudinal control of autonomous vehicle motions [18], sliding order and sliding accuracy in sliding mode control [19], finite time stability and robust control synthesis of uncertain switched systems [20], nonlinear distance and cruise control for passenger cars [21], smooth second-order sliding modes: Missile guidance application [22]. Autonomous vehicles (AVs) require accurate dynamic models to operate safely and efficiently under diverse conditions, especially at driving limits.