On the Analytical Properties of a Nonlinear Microscopic Dynamical Model for Connected and Automated Vehicles

In this letter, we propose an integrated dynamical model of Connected and Automated Vehicles (CAVs) which incorporates CAV technologies and a microscopic car-following model to improve safety, efficiency, and convenience. We rigorously investigate the analytical properties such as well-posedness, maximum principle, perturbation, and stability of the proposed model in some proper functional spaces. Furthermore, we prove that the model is collision-free and derive an explicit lower bound on the distance as a safety measure.