# Adaptive Global Fast Sliding Mode Control for Steer-by-Wire System Road Vehicles
## 1 Introduction  
The automobile industry is immensely working to transform conventional road vehicles into partial/full autonomous vehicles. SAE International and NHTSA have classified six levels of driving autonomy from \"no automation\" to \"full automation\" [1; 2]. In particular, from the lane-keeping assistance system [3] to fully automated maneuvering [4; 5; 6], Steer-by-Wire (SbW) technology is playing a fundamental role in advanced driving assistance systems [7]. Nissan introduced the first commercialized SbW system in 2013 with the Infiniti Q50 vehicle [8; 9]. The SbW system delivers better overall steering performance with comfort, reduces power consumption, provides active steering control, and significantly improves the passenger safety. Compared with a conventional steering system, the SbW system has replaced the mechanical shaft between the steering wheel and front wheels with two actuators, controllers, and sensors. The first actuator steers the front wheels and the second actuator provides steering feel feedback to the driver, obtained from the road and tire dynamics. Over the last decade, many researchers have proposed a number of control techniques to compensate for the system parameter variation, change in road conditions, and external disturbances for obtaining the robust performance of the SbW system. In [10; 11], sliding mode based control schemes are proposed for a partially known SbW system with unknown lumped uncertainties to track the reference signal. However, it is hard to classify the wide range of nominal parameters under the sideslip, and the robust performance may not be guaranteed over different road conditions. In [12; 13; 14; 15; 16], the upper bound sliding mode control (SMC) technique is proposed for the bounded unknown SbW system parameters and uncertain dynamics. However, the process of obtaining these proper bounds is not evident. In [17; 18; 19; 20] proportional-derivative (PD) control is proposed to follow the driver's steering wheel signal closely. However, under uncertain dynamics, it is difficult to achieve satisfactory performance with a conventional control scheme. In [21] cornering stiffness and chassis side slip angle are estimated to calculate the self-aligning torque. The authors used the proportion of estimated torque as a feedback to the driver for artificial steering feel. In [22] three suboptimal sliding mode techniques are evaluated for yaw-rate tracking problem in over-actuated vehicles. In [23; 24], adaptive control is implemented for path tracking via SbW system and the authors estimated the sliding gains by considering the known steering parameters and cornering coefficients. However, they did not use any mechanism to stop the estimation. Consequently, the controller could lead to saturation by estimating too large a sliding gain. In [25; 26] the authors proposed a hyperbolic tangent function with adaptive SMC based schemes to counter the effect of self-aligning torque. In [27] the frictional torque and self-aligning torque are replaced by a second-order polynomial function that acts as an external disturbance over the SbW system. The authors proposed an adaptive terminal SMC (ATSMC) to estimate the upper bounds of parameters and disturbance. Apart from the control design, a robust estimation methodology is also needed for the SbW system to estimate the vehicle states, uncertain parameters, and tire-road conditions for eliminating the effect of external disturbances from the controller. For instance, in recent years Kalman filter (KF) and nonlinear observers have gained much more attention from researchers; for example, in [28] a dual extended KF is used to estimate vehicle states and road friction. In [29] the authors estimated five DOF vehicle states and inertial parameters, such as overloaded vehicle's additional mass, respective yaw moment of inertia, and its longitudinal position using the dual unscented KF by considering the constant road-tire friction over a flat road.