Safety-Critical Control of Connected Vehicle Systems Based on Barrier Functions

Platooning control of connected vehicle systems (CVSs) exhibits great potential in reducing vehicle spacing and improving road throughput. The control performance of CVSs, including stability, string stability, speedability, and scalability—known as the 4S performance indices—has been extensively studied. However, potential safety threats associated with platooning control, such as avoiding collisions during the state convergence process, have not been fully addressed. Specifically, balancing the control performance and safety within CVSs is a challenging problem. In this paper, a distributed nominal controller is initially designed based on the linearized third-order vehicle dynamics model to achieve the 4S performance indices. The collision-free safety state set (SSS) for the platoon is constructed by designing pairwise safety barrier certificates, grounded in the physical constraints of vehicle acceleration. To ensure the forward invariance of the SSS while minimizing control performance degradation, the exponential control barrier function (CBF) is employed to design the centralized safety-critical controller. Specifically, quadratic programming is applied to determine the optimal solution that satisfies the safety barrier constraints while deviating minimally from the nominal controller. To enhance the scalability and reduce the computational complexity, constraints of control input are distributed to individual vehicles with the help of the decentralized safety barrier certificate. Furthermore, explicit solutions for the decentralized safety-critical controller are derived using the Karush-Kuhn-Tucker (KKT) condition. Simulation scenarios containing different spacing control strategies are provided to validate the effectiveness of the theoretical results in this paper.