Jam traffic pattern of a multi-phase lattice hydrodynamic model integrating a continuous self-stabilizing control protocol to boycott the malicious cyber-attacks

While connected-automated vehicles (CAVs) can share traffic data with external nodes through vehicle-vehicle or vehicle-infrastructure communication, the exoteric workshop communication setting makes the vehicles susceptible to cyber-attack interference, which will affect the normal information interaction between vehicles. Besides, in practice, the driver uses the accelerator, gear shift lever or brake pedal to accelerate and decelerate the vehicle, whereas the complex piecewise acceleration process is negligible in existing works. In doing so, we use historical traffic information to compensate for the missing core data caused by malicious cyber-attacks. We then propose a novel multi-phase lattice hydrodynamics model considering malicious cyber-attacks. A switch continuous self-stabilizing security control protocol is embedded to reinforce the steadiness of traffic flow. The typical optimal velocity function, which frequently serves as a basic hyperbolic tangent function, is swapped with a two-stage (three-phase) optimal velocity function to elucidate the intricate three-phase traffic flow system. Following the linear stability theorem, the critical stability criteria for the new model are identified. The outcome reveals that the cyber-attack intensity and control gain coefficient have profound effects on the steadiness of traffic flow, and the stage of phase transition is determined by what amount of turning points are contained in the optimal velocity function. The modified Korteweg–de Vries (mKdV) equation that indicates the density wave in a bottleneck area is established with the aid of nonlinear stability analysis and the associated analytical solution is obtained. Numerical studies have been conducted under periodic boundary circumstances to verify the correctness of the mathematical analysis.