On the Chain Stability of Bilateral Control Model

In this paper, we study the chain stability of vehicles under bilateral control (BCM), and prove that vehicles under bilateral control are chain stable, i.e., all input perturbations to the chain decay exponentially (with the length of the chain). Chain stability analysis tells us how vehicles under bilateral control will act in traffic when mixed with cars driven by human drivers. It shows that self-driving cars using bilateral control can reduce traffic flow instabilities in mixed traffic. Indeed, chains of BCM vehicles become perturbation-consuming dampers when inserted in traffic, since they split chains of human-driven vehicles and prevent perturbations from being transmitted from one chain of car-following cars to the next. Thus, today's traffic can be improved greatly by the insertion of BCM vehicles. The simulation results validate the theoretical analysis.