Proportional Spacing Tracking Control for Connected Vehicle Platoons Under Semantic Deception Attacks

Connected vehicle platoons rely on intervehicle information to regulate longitudinal spacing and attenuate downstream disturbance propagation. This dependence also exposes the platoon to semantic deception attacks that falsify communicated gap and relative speed information while preserving kinematic consistency. This paper investigates proportional spacing tracking and velocity string stability for a predecessor-following platoon of third-order vehicles with first-order actuator dynamics under such attacks. A vehicle-dependent proportional spacing policy is developed in which the proportional factor acts exclusively on the desired spacing without scaling the leader state. The semantic falsifications are mapped through the distributed controller into an equivalent attack-induced input while their kinematic coupling is retained in the closed-loop model. Internal stability is characterized using the Routh–Hurwitz criterion, and verifiable sufficient conditions for nominal velocity string stability are derived through frequency-domain analysis. A weighted transfer-gain inequality is further established to characterize the propagation of finite-energy semantic deception. By applying Parseval’s relation, the frequency-domain bound is converted into an explicit L2 energy recursion relating link-wise attack energy to downstream velocity-deviation energy. The resulting conditions clarify how the time headway, proportional spacing factor, actuator time constant, and feedback gains jointly affect the velocity string-stability margin.