Formation control of longitudinal vehicular platoons under generic network topology with heterogeneous time delays

The problem of third-order consensus of homogeneous vehicular platoons in the presence of communication and parasitic delays is investigated. The communication topology of vehicular networks is assumed to be directed and generic. Therefore, a number of eigenvalues of the network's matrix are complex, entangling the stability analysis of the closed-loop dynamics. By considering both communication and parasitic delays, a new linear centralized consensus protocol is designed for each vehicle. It will be shown that the closed-loop dynamics of vehicular networks with generic topology is in the form of linear systems with multiple delays. By presenting a new approach, the resultant linear time delay system is decoupled to individual third- and sixth-order dynamical equations. By performing the stability analysis of the new equations, it will be proven that the control parameters are independent of the network's topology. Therefore, the control design and stability analysis will be significantly simplified compared with previous studies. To find the stable regions of time delay, the cluster treatment characteristic root method is employed. Simulation results are provided to show the effectiveness of the proposed approach.