String stable control design for automated vehicles under cyberattacks

Emerging automated vehicle (AV) technologies open a door for cyberattacks, where a select number of AVs are compromised to drive in an adversarial manner, degrading the performance of transportation systems. Hence, designing stable controls for AVs that can mitigate the impact of attacks on traffic flow is important and necessary as AVs gradually become a reality. In this study, we first present a general framework for describing mixed-autonomy traffic involving AVs and human-driven vehicles (HVs) based on car-following dynamics. Under this framework, a class of malicious attacks on AV control commands (vehicle acceleration) is mathematically characterized. To deal with the lack of knowledge of the attacks, we model attacks as an unstructured process, allowing for the inclusion of both deterministic and stochastic attack behaviors, bounded by a known bound (to remain stealthy) without being subject to any specific statistical distribution. Moreover, we analytically derive a set of sufficient conditions for string stable control design of individual AVs which can help mitigate the disturbances to traffic flow caused by unknown attacks on AVs. Furthermore, for any given market penetration rate of AVs, a set of conditions is also derived for selecting appropriate feedback gains of AVs to ensure string stability of heterogeneous traffic, reducing the undesired impact of attacks on traffic flow. These sufficient conditions provide important criteria for string stable control design of AVs without requiring much knowledge of the attacks. A series of numerical results is presented to show effectiveness of the proposed approach on mitigating attack disruption.