Socially Optimal Linear Quadratic Control With Resilience for Vehicle Platooning

The growing deployment of networked multi-vehicle systems for autonomous mobility and logistics underscores the need for robust and resilient control under adversarial and uncertain conditions. Vehicular platooning offers benefits in traffic efficiency, energy savings, and safety; yet, conventional equilibrium-based control schemes remain vulnerable to cyber-physical attacks such as jamming, spoofing, and denial-of-service (DoS), threatening reliable coordination. In this paper, we propose a socially optimal linear-quadratic (LQ) control framework that embeds collective performance objectives directly into the quadratic cost formulation. This approach targets operating configurations that reflect platoon-level social optimality, which may differ from the closed-loop equilibrium. This results in an extended LQ tracking formulation that steers the platoon toward the equilibrium closest, in a quadratic sense, to the socially optimal configuration. To counter adversarial conditions, we integrate resilience mechanisms against cyber-physical attacks—including false data injection (FDI), spoofing, and jamming—addressing attacks directed at the supervisory unit and individual vehicles. Simulation results demonstrate the effectiveness, robustness, and practical implementability of the proposed approach in both nominal and adversarial scenarios. Note to Practitioners—Vehicle platooning, where multiple vehicles travel in close coordination, has been recognized as a promising solution to improve road safety, reduce fuel consumption, and increase traffic efficiency. However, today’s platooning systems face two major challenges: 1) conventional control strategies are typically designed around fixed operating points, which optimize local or individual objectives and may fail to capture socially optimal platoon-level performance; and 2) reliance on wireless communication makes platoons vulnerable to cyber-physical disruptions such as spoofing, jamming, or false data injection. This paper addresses these challenges by introducing a socially optimal linear-quadratic (LQ) control framework that explicitly embeds collective performance objectives into the control design. This framework enables platoons to operate around configurations that reflect socially optimal speed and spacing policies, which may differ from the equilibrium of the closed-loop system. In addition, we integrate resilience mechanisms into the control strategy to ensure that the platoon remains stable and coordinated even under attacks targeting the supervisory unit and individual vehicles. The proposed methods have been validated through simulations and are particularly relevant for industrial applications involving heavy-duty truck platoons, autonomous mobility fleets, and smart logistics. The main practical benefits include improved social efficiency, safer inter-vehicle coordination, and enhanced resilience against attacks on both the vehicles and the supervisor-vehicle communications link. While our study focuses on performance evaluation via simulation, the approach is computationally efficient and suitable for real-time implementation, making it a strong candidate for future deployment in intelligent transportation systems. Future work will involve real-time hardware-in-the-loop (HIL) validation and extending the framework to formally account for time delays.