A new virtual leader-following consensus protocol to internal and string stability analysis of longitudinal platoon of vehicles with generic network topology under communication and parasitic delays

In this paper, a new virtual leader following consensus protocol is introduced to perform the internal and string stability analysis of longitudinal platoon of vehicles under generic network topology. In all previous studies on multi-agent systems with generic network topology, the control parameters are strictly dependent on eigenvalues of network matrices (adjacency or Laplacian). Since some of these eigenvalues are complex, the stability analysis with the presented methods is very hard or even impossible for large scale or time-varying networks. A new approach is introduced in this paper to decouple the large dimension closed-loop dynamics to individual third-order linear differential equations. A new spacing policy function assuring safety and increasing the traffic capacity is introduced to adjust the inter-vehicle spacing. The stable regions of communication and parasitic delays are calculated by employing the cluster treatment characteristic roots (CTCR) method. In addition to internal stability, it will be shown that the presented approach guarantees the string stability of generic vehicular networks. The most important privilege of the presented method compared with the previous approaches, is that the control gains are independent on network structure. This new finding, simplifies the stability analysis and control design specially for large scale platoons and time-varying networks. Several simulation results are provided to show the effectiveness of the proposed approaches.