# Enhancement of Yaw Moment Control for Drivers with Excessive Steering in Emergency Lane Changes
## 1 Introduction  
The active safety system in vehicles is a key aspect of vehicle dynamics control. It comprises two primary categories based on their relevance to driving conditions (see [1, 2] and references therein). The first category involves auxiliary control of the vehicle's longitudinal motion to prevent wheels from locking or slipping due to a driver's excessive braking or traction. Well-known examples of such systems include the Anti-lock Brake System (ABS) and Traction Control System (TCS). The second category is Vehicle Stability Control (VSC), which stabilizes the lateral motion of the vehicle by controlling its body sideslip angle and yaw rate. The development of VSC is motivated by the fact that most drivers lack the ability or experience to manage sudden skids while driving. When a driver makes an emergency lane change in panic, they may overreact and steer too aggressively. This can cause the tire/road friction to saturate, resulting in the vehicle skidding sideways and potentially colliding with other vehicles or crash barriers. There are three main approaches to stabilizing vehicle lateral motion in literature. The first approach involves using differential torque between the left and right wheels to produce DYM for stabilization. Control design methods for DYM stabilization includesliding mode control [3], model predictive control [4; 5], LPV control [6; 7], and other techniques (see [1; 2; 3; 4; 5; 6; 7] and references therein). The second approach is to manipulate the steering angle to achieve lateral motion stabilization. Active Front Steering (AFS), Active Rear Steering (ARS), and Four-Wheel Steering (4 WS) are examples of this approach (see [8; 9; 10; 11] and references therein). In AFS, for instance, a compensation steering angle is coupled to the driver steering angle through the planetary gear mechanism to adjust the front-wheel steering angle. The third approach combines an active wheel steering scheme with the DYM method (see [12; 13; 14] and references therein). This integration method adjusts the longitudinal and lateral tire/road frictions simultaneously within the linear friction region, effectively stabilizing the vehicle's lateral state and providing promising performance. However, directly integrating AFS may lead to excessive steering of the front wheels, particularly when the driver steers aggressively in a moment of panic. In such scenarios, the literature often relies solely on the DYM method and treats the driver's excessive steering as an external disturbance. As a result, the DYM method has to dedicate most of its capacity to counteracting the instability caused by excessive steering, thereby reducing its effectiveness in managing other stabilization factors concurrently. On the other hand, time-varying vehicle speed is a significant factor of the vehicle's lateral dynamics. During an emergency intervention, the vehicle speed is usually constantly changing. Although certain controllers have been developed to ensure performance around constant vehicle speeds, they might not be theoretically appropriate for situations where the vehicle speed changes over time. In the literature, a modeling technique with the polytopic LPV is often used to deal with the situation of time-varying vehicle speed (see [6; 7] and references therein). The polytopic LPV control offers the advantage of applying linear control techniques to nonlinear systems. This type of controller design often employs a quadratic Lyapunov function, in which the Lyapunov matrix is constant or parameter-dependent, to ensure some specific performance across an interested polytope. When the parameter varies within the polytope, the design and analysis of the controller can be focused solely on the polytope vertices. This approach guarantees the stabilization of every parameter point within the polytope. The polytopic LPV control design is typically performed with rectangular polytopes.