## 1 Introduction  
Lateral control systems for high-performance vehicles are developed to prevent the driver from losing control of the vehicle and to improve the cornering agility of the vehicle. Nevertheless, front-wheel drive (FWD) high-performance cars can be developed in combination with high-power engines based on existing small vehicle platforms or subcompact vehicle platforms [1]. Therefore, such FWD high-performance cars can be developed at a relatively low cost. However, the inner wheels of FWD vehicles spin when a driving torque greater than the inner-wheel grip is applied due to the weight transfer during acceleration while turning. This spinning results in understeer and a reduction in exit acceleration.  
This can be overcome by controlling the inner-wheel slip via an electronically limited slip differential (ELSD) when the inner-wheel speed becomes greater than the outer-wheelspeed and spins during an accelerated exit. The ELSD can apply friction torque to restrict the rotational degrees of freedom of the left and right wheels [2]. Wheel torque is reduced when the wheel spins without traction by transferring the driving torque from the fast shaft to the slow shaft when the degrees of freedom of the left and right wheels are restricted by the friction torque. Therefore, the torque can be transferred to the wheel that has traction. However, if control is performed after the wheel slip occurs, then the initial wheel spin cannot be controlled properly because of the time delay in the system operation. Thus, a controller that can predict inner-wheel slipping in advance and perform appropriate pre-emptive control is needed.  
We created a control algorithm that predicts inner-wheel spinning during acceleration while turning by calculating the friction limit at which the inner wheel can be driven in real time [3]. A concept is designed for the ELSD clutch to engage based on the difference between the real driving force from the powertrain and the allowable driving force of the inner wheel, as shown in Figure 1.  
The accuracy of the wheel spin predictive control can be improved by predicting the friction coefficient of the road surface. In addition, one of the factors that greatly affect the driving and safety performance of a vehicle is the real-time change in the tire-road friction coefficient. The vehicle motion caused by steering, traction, and braking forces of the vehicle is affected by the tire-road friction coefficient. Therefore, tire-road friction coefficient information is important for the performance of the vehicle control system. If the vehicle is driven in an unusual road environment, the driving system will fail to produce the original performance, which results in an unstable vehicle control process.  
If the accurate estimation of the tire-road friction coefficient is possible, vehicle control performance can be stabilized through better system operation. The vehicle predictive control system automatically adjusts the timing and amount of system intervention by reflecting the friction characteristics of the road surface changes, thereby maximizing the functionality of the control system. Therefore, various research efforts are underway to ensure the stable performance of vehicle driving systems by estimating the tire-road friction coefficient using different methods.