###### Abstract
Specifically, all components of the steering system should possess fault-tolerant features to accommodate at least one failure [27]. One potential solution to this challenge is to employ multiple identical units operating in parallel. In the event of a failure in one unit, the backup units can seamlessly take over, ensuring continued operation. However, this solution comes with added costs and results in an increase in system volume. An alternative approach to enhancing reliability without adding weight or cost to the system is to utilize estimation techniques, including the implementation of state observers [27]. In this paper, motivated by the published work of time-varying ADRC design in [28], a novel time-varying adaptive gain ADRC is proposed for the uncertain nonlinear SBW plant under communication time delays. The proposed AADRC has two components: the adaptive ESO (AESO) and adaptive full-state error feedback control (AFSEFBC). The main contributions are summed up as follows:  
1. Large time delays in a communication channel that the second-order SBW suffers are considered, therein a first-order Taylor series expansion is introduced to address the time delays. However, the order of SBW becomes three; thus, the increase in system order makes the control tasks more complicated. To solve the complexity arising from the Taylor approximation, we propose a novel active disturbance rejection control (AADRC) for the time-delayed SBW subject to system uncertainties and disturbances from external factors. 2. Because of consideration and approximation of the time delays, the overall disturbances acting on the SBW become very large. To overcome this issue, we lump the nonlinearities, uncertainties, and external disturbances of the SBW that are separated from the total disturbances. Such separation of disturbances makes the feasibility of application of the novel AADRC which is a combination of AESO and AFSEFBC. 3. A novel AESO is proposed to estimate unmeasured velocity and acceleration, as well as the lumped disturbance with better estimation precision, low computation cost, and minimum peak phenomenon. Adaptive gains of the AESO are updated online based on a position estimation error to improve estimation performance. 4. A novel AFSEFBC is improved to enhance the trajectory tracking efficiency of the angular steering position of the front wheel, in which its gains are adjusted online according to the position tracking error, and thus the angular steering position is improved in terms of lesser overshoot and better steady state. 5. The boundedness of the estimation and the tracking error of the closed-loop stability of the AESO and AFSEFBC, respectively, is rigorously analyzed. Finally, two simulation cases with a comparison with the standard ADRC are carried out to show the validity of the suggested AADRC scheme. The remainder of this text is structured as follows: Section 2 introduces the SBW plant represented by the benchmark simulation model. Section 3 presents the novel adaptive ADRC design procedure for the time-delayed SBW system, which is divided into subsections of designing AESO and AFSEFBC. In this section, the boundedness of estimation and tracking errors of the AESO and AFSEFBC, respectively, are analyzed. Then, in Section 4, the efficiency and feasibility of the proposed control scheme are validated by simulation results from the simulative SBW vehicle. Finally, Section 5 describes the conclusions of this full text with future work.