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.