Optimal feedback control law for automated vehicles in the presence of cyberattacks: A min–max approach

While automated vehicles (AVs) are expected to bring a wide range of benefits to future transportation systems, emerging AV technologies open a door for cyberattacks, where a select number of AVs are compromised to drive in an adversarial manner. This could result in network-wide increases in traffic congestion and energy consumption, degrading the performance of transportation systems. Hence, it is necessary to develop attack mitigation strategies for AVs as AVs gradually become a reality. However, this is rather challenging due to the lack of knowledge of adversaries. Limited prior studies have assumed attacks with a given probability distribution without considering their malicious intention, which is far from realistic due to the adversarial nature of potential attacks. In this study, we derive an optimal feedback control law for AVs in the presence of cyberattacks. Notably, attacks are only assumed to have a bounded magnitude without being subject to any specific statistical distribution, which is not only of theoretical interest but also relaxes the assumptions seen in prior studies. More importantly, to deal with lack of knowledge of malicious attacks, we, for the first time, formulate a min–max control problem to minimize the worst-case disturbance to traffic flow. Specifically, we present a mathematical framework for describing mixed-autonomy traffic involving AVs and human-driven vehicles (HVs), considering two typical types of attacks, namely false data injection attack on sensor measurements and malicious attack on AV control commands. Based on the framework presented, we derive a set of necessary conditions of optimality for the min–max control problem, based on which an iterative computational algorithm is developed for determining the optimal control (driving) strategy of AVs. The effectiveness of the proposed approach is demonstrated via extensive numerical simulations.