Analysis of Automotive Cyber-Attacks on Highways Using Partial Differential Equation Models

This paper considers scenarios wherein a group of malicious vehicles on a highway perform a cooperative attack with the motive of creating undesirable wave effects among other vehicles on the highway. The two species of vehicles-malicious vehicles and normal vehicles, and their associated interaction effects-are modeled using partial differential equations. The malicious vehicles, which may be arbitrarily distributed on the highway, perform a sequence of velocity changes with the objective of making the density/velocity profile on the highway, track a reference profile. This reference profile (chosen by the malicious vehicles) has the property that once generated, it spontaneously evolves into a shock wave that propagates along the highway. Analytical expressions governing the velocity inputs of the malicious vehicles with which they can generate such waves are determined, for perfect as well as imperfect information scenarios. Simulation results are presented to validate the theory.