# Enhancement of Yaw Moment Control for Drivers with Excessive Steering in Emergency Lane Changes
## 1 Introduction
However, when the actual parameter trajectories do not reach certain vertices of the rectangular polytope, such as the vehicle speed parameter in the LPV vehicle control design, some studies suggest reducing the polytope size and using other forms of polytopes like trapezoidal, triangular, or two-vertex polytopes for the design (see [6] and references therein). The LMI technique usually accompanies the polytopic LPV control design to find feedback gains that satisfy design specifications [6; 7; 15; 16]. Reference [7] developed a lateral reference state tracking control using the polytopic LPV-LMI modeling and gain scheduling method. It copes with issues of cornering stiffness uncertainty by using a norm-bounded structured uncertainty approach. However, the reference state provided in the study does not include safety limit ranges. As a result, when the driver's steering angle exceeds a certain threshold, the corresponding reference state will exceed the safety range. Therefore, their proposed solutions are more suitable for driving circumstances where the driver's steering angle falls within a normal operation range. This study proposes an active safety control system to handle emergencies where the driver applies excessive steering input and the vehicle speed changes significantly during control. The system combines the DYM method with a steering saturation scheme to prevent excessive driver steering input from affecting the wheel steering angle. This approach keeps the tire/road friction within the linear operation range during emergencies and enables the DYM to allocate more capacity to other stabilization control tasks. The control system uses a reference state as well as a reference steering angle, obtained from the steady state of a linear vehicle lateral model and from the limitations imposed by tire/road friction saturation, to guide its operation. When the driver's steering angle and the system state diverge from the established reference values, the control system steps in by implementing both the steering saturation scheme and the DYM method. Thisintervention maintains the front-wheel steering angle and system state in close alignment with the reference values. To deal with the problem of varying vehicle speeds, this study employs the polytopic LPV modeling technique. The Lyapunov redesign concept is also utilized to decompose overall uncertainties into structured uncertainties of matching and unmatching conditions (see [17; 18; 19] and references therein). This simplifies the controller design process. Moreover, the design of the DYM control with input constraint uses numerical solutions to LMIs, with the restriction on the DYM value obtained by considering the limit condition of the friction circle on the combined wheel slip. Once the design is finalized, an input saturation technique utilizing a high-gain approach is employed to enhance control utilization and improve system response during emergency situations [20; 21]. Finally, the resulting yaw moment is distributed to the four wheels to generate the wheel control torque. The results from simulation indicate that the enhanced integration strategy achieves not only safety reference state tracking, but also ensures the tire/road friction operates in its linear range and enables the DYM to handle more instability factors. This article presents two primary contributions. First, it proposes a control system designed to compensate for excessive driver steering by using the reference steering angle. This approach ensures that the front-wheel steering angle remains within a safe range while regulating the yaw moment to minimize deviations between the safety reference state and the vehicle's actual state. Integrating these controls also keeps tire/road friction within a manageable linear range, allowing the DYM to focus on other stabilization tasks. Second, the study introduces a high-gain input saturation technique aimed at enhancing the efficiency of the control law when faced with input constraints.