Jams and phase transitions in heterogeneous lattice model integrating the continuous delayed feedback control to boycott cyber-attacks under connected autonomous and human driven vehicles environment

As traffic systems are becoming increasingly interconnected and automated, the heterogeneous traffic flow consisting of the connected autonomous vehicles (CAVs) and human driven vehicles (HDVs) will be the main mode of transportation. But, CAVs face significant susceptibility to malicious cyber-attacks, which could cause worse traffic jams and accidents. Thus, utilizing the lattice hydrodynamic framework, we create an innovative lattice model by integrating a continuous delay feedback control to mitigate the negative impact of cyber-attacks on the heterogeneous traffic flow. Through theoretical analysis involving linear stability analysis and nonlinear analysis, we derive the neutral stability condition and modified KdV equation of new lattice model. Additionally, numerical simulation is carried out to check the theoretical results. Simulation results show that the stability of heterogeneous traffic flow descends or the roadway efficiency diminishes after an attacker tampers with the density information received from CAVs. However, the designed control method can effectively resist the interference of cyber-attacks on heterogeneous traffic flow and improve traffic system stability and efficiency. Moreover, we firstly quantitatively assess the stability of traffic flow via the methodologies of power spectrum analysis and spectral entropy, offering valuable insights for the refinement of traffic management paradigms.