###### Abstract  
In this paper, an adaptive active disturbance rejection control is newly designed for precise angular steering position tracking of the uncertain and nonlinear SBW system with time delay communications. The proposed adaptive active disturbance rejection control comprises the following two elements: (1) An adaptive extended state observer and (2) an adaptive state error feedback controller. The adaptive extended state observer with adaptive gains is employed for estimating the unmeasured velocity, acceleration, and compound disturbance which consists of system parameter uncertainties, nonlinearities, exterior disturbances, and time delay in which the observer gains are dynamically adjusted based on the estimation error to enhance estimation performances. Based on the accurate estimations of the adaptive extended state observer, the proposed adaptive full state error feedback controller is equipped with variable gains driven by the tracking error to develop control precision. The integration of the advantages of the adaptive extended state observer and the adaptive full state error feedback controller can improve the dynamic transient and static steady-state effectiveness, respectively. To assess the superior performance of the proposed adaptive active disturbance rejection control, a comparative analysis is conducted between the proposed control scheme and the classical active disturbance rejection control in two different cases. It is worth noting that the active disturbance rejection control serves as a benchmark for evaluating the performance of the proposed control approach. The results from the comparison studies executing two simulated cases validate the superiority of the suggested control, in which estimation, tracking response rate, and steering angle precision are greatly improved by the scheme proposed in this article. s 2  
the driver's intended actions and even make the system unstable. Therefore, the enhancement of the front wheels' tracking accuracy and robustness against uncertainties emerge as crucial research topics in the SBW systems [5]. To bolster the tracking precision and robustness of various sources of uncertainty, the disturbance/uncertainty estimation and attenuation (DUEA) techniques have been garnering significant attention over the past several decades. It is worth noting that active disturbance rejection control (ADRC), as well as disturbance observer-based control (DOBC), fall under the umbrella of DUEA techniques [6], i.e., an observation methodology is established to estimate the disturbances or uncertainties, with the estimation results then utilized to compensate for uncertainties within a robust controller. In [7], the ADRC is effectively utilized to ensure precise control of the angular position of the front wheels, enabling them to accurately follow the movements of the steering wheel against uncertainties such as the self-aligning torque. To enhance the controller's robustness even further, sliding mode control (SMC) is seamlessly integrated into the ADRC in [8]. To enhance the convergence rate of the SMC, the fractional-order SMC is introduced in the SBW system to enhance the integral and derivative actions, thereby increasing the parameter optimization space and improving tracking performance [4]. In these references, the extended state observer (ESO) is adopted in ADRC to compensate for uncertainties. Due to the potential presence of extensive unknown nonlinearities and uncertainties in SBW systems, refs. [9; 10] considered the application of neural networks (NNs) to enhance the SBW systems' uncertainty estimation performance. The underlying rationale is that NNs possess the remarkable capability to approach various functions with arbitrary precision under specific conditions. Please notice that the controller gains mentioned in the literature above are constant, i.e., they are fixed values and determined before operating the control algorithms. Adaptive control belongs to crucial control methodology to deal with time-varying model parameters [2; 11].