Estimation and Expansion of Vehicle Stability Region With Sums of Squares Programming

The vehicle stability region can be used to evaluate vehicle stability performance and lay the foundation for vehicle safety improvement. It can be obtained via the region of attraction (RoA) based on sums of squares (SOS) programming. However, it is usually conservative, and the computational burden is large. This article focuses on the above issues and proposes a well-developed method for RoA estimation, with application to the estimation and expansion of the vehicle stability region. For RoA estimation, an improved SOS program is formulated, and its optimization objective combined with the customized algorithm significantly reduces conservatism. In addition, the feasibility prejudgment strategy and the dynamic search range are proposed in the algorithm. As a result, the computational burden is greatly reduced, which also indirectly helps reduce conservatism. Then, a more accurate vehicle stability region is obtained with less time consumption, and a map-based controller is proposed to improve vehicle stability. Better stability performance and larger stability regions are guaranteed under different scenarios due to the adaptive adjustment of controller gains. Finally, simulations and hardware-in-the-loop experiments with an embedded vehicle controller are performed to verify the effectiveness of our method.