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Third-order leader-following consensus protocol of traffic flow formed by cooperative vehicular platoons by considering time delay: constant spacing strategy

In this article, the problem of third-order consensus of homogeneous traffic flow formed by cooperative vehicular platoons is studied. This article is presented in two main parts. Inter-platoon stability analysis and intra-platoon stability analysis. For inter-platoon stability analysis, due to great length of traffic flow, it is assumed that lead vehicle is not available. Therefore, a new consensus algorithm based on bidirectional virtual leader-following strategy is introduced. Both communication and parasitic delays are involved in control design and stability analysis. By decoupling the closed-loop dynamics of cooperative leaders and employing the cluster treatment characteristic root method, necessary conditions on control parameters and stable regions of time delay satisfying internal stability of leaders’ network are derived. In continuance of this part, inter-platoon string stability is studied. In the second part, it is assumed that the communication topology of each platoon is generic. Therefore, some of the eigenvalues of network matrix are complex which complicates the intra-platoon stability analysis. After decoupling the closed-loop dynamics of each platoon, a new consensus algorithm is presented. It will be shown that by this algorithm, the control parameters are independent of eigenvalues of network matrix which simplifies the controller design and stability analysis. Several simulation results are provided to show the effectiveness of the proposed approaches.