## 1 Introduction
The sliding mode controller (SMC), because of its high robustness and finite time convergence, can converge in uncertain disturbance systems and has been applied into practical engineering [19; 20; 21]. However, in the case of severe system disturbance, a large robustness coefficient should be selected during the design of smcs, but this will cause serious vibration. To solve this problem, researchers have changed the criterion of robustness coefficient selection from uncertainty disturbance to the approximation error of system disturbance, which will reduce the robustness coefficient and system vibration. Recently, the uncertainty disturbance during practical engineering modeling has been extensively studied. The uncertainty of tire rigidity upon vehicle steering can be described by the norm constraint [22]. The nonlinear disturbance of systems was handled by combining the robust integration of an error controller with the adaptive controller [23]. During wheel slip tracking control, a radial basis function neural network (RBFNN) was used as an uncertainty observer to estimate the uncertainty during modeling [24]. A linear uncertainty vehicle model with steering rigidity uncertainty was built [25]. A function recursive fuzzy neural network uncertainty estimator [26] and a self-organizing function-link fuzzy cerebellar model articulation controller [27] were used to approximate the unknown nonlinear terms of vehicle dynamics during ABS control. Nonlinear adaptive backstepping control algorithms based on model parameter adaptive controller with slide mode observer [28] and on dynamic recursive radial basis function network uncertainty observer [29] were designed and used to observe the nonlinear uncertainty of permanent magnet direct-current generators. The above studies about uncertainty approximation are focused on a certain aspect of uncertainty, and the algorithms still should be improved further. As for systemic uncertainty, it can be approximated in both fuzzy systems and RBFNN systems. The ad vantage of fuzzy systems lies in the strong ability of fuzzy language utilization, which endows fuzzy systems with high inferring ability. In comparison, RBFNN systems possess strong generalization ability and simple network structures and can avoid unnecessary or redundant computation. By integrating the strong inferring ability of fuzzy systems and the strong learning ability of rbfnns, we proposed a fuzzy radial basis function neural network (FRBFNN) for uncertainty approximation. The vehicle stability control algorithm proposed in this study is structurally illustrated in Figure 1. Firstly, a 7-degrees-of-freedom (DOF) nonlinear dynamic vehicle model based on the unitire model was built. Based on the parameters directly monitored by vehicle sensors and the 7-DOF model, we designed an ADUKF algorithm and used it to estimate the sideslip angle. Secondly, based on a 2-DOF linear vehicle reference model, the ideal values of the stability control parameters were outputted. Given the uncertainty of system modeling, we adopted a 2-DOF nonlinear vehicle model involving system uncertainty and additional yaw moment, and established an adaptive fuzzy radial basis function neural network sliding mode control (AFRBF-SMC), which was used to trace and control the ideal values of the control parameters. After the additional yaw moment was calculated by the controller, the braking torque was allocated according to the judgement of vehicle status, and the wheel cylinder pressure was outputted via the execution layer to the vehicle model. Thereby, closed-loop control of the vehicle stability system was accomplished.