Stabilizing Traffic with Autonomous Vehicles

Autonomous vehicles promise safer roads, energy savings, and more efficient use of existing infrastructure, among many other benefits. Although the effect of autonomous vehicles has been studied in the limits (near-zero or full penetration), the transition range requires new formulations, mathematical modeling, and control analysis. In this article, we study the ability of small numbers of autonomous vehicles to stabilize a single-lane system of human-driven vehicles. We formalize the problem in terms of linear string stability, derive optimality conditions from frequency-domain analysis, and pose the resulting nonlinear optimization problem. In particular, we introduce two conditions which simultaneously stabilize traffic while imposing a safety constraint on the autonomous vehicle and limiting degradation of performance. With this optimal linear controller in a system with typical human driver behavior, we can numerically determine that only a 6% uniform penetration of autonomously controlled vehicles (i.e. one per string of up to 16 human-driven vehicles) is necessary to stabilize traffic across all traffic conditions.