Control design and stability analysis of homogeneous traffic flow under time delay: A new spacing policy

Abstract

This paper details control design and stability analysis of homogeneous traffic flow by considering it as the interaction between inter-connected vehicular platoons. A third-order linear differential model is used to describe the longitudinal motion of each vehicle. As the lead vehicle of the whole traffic flow may be not available, the inter-platoon communication structure is assumed to be a bidirectional virtual leader following (BDVLF) topology. Both communication and parasitic delays are considered in the system modeling and control design. By employing an appropriate state transformation, the 3N-order closed-loop dynamics are decoupled to N third-order dynamical equations. The cluster treatment characteristic root (CTCR) method is employed to perform the inter-platoon stability analysis. The intra-platoon communication structure is assumed to be general. Therefore, the eigenvalues of matrix H maybe complex which makes the stability analysis more intricate. By introducing a new decoupling approach and applying a centralized control for each vehicle in the platoon, the necessary conditions on control parameters satisfying intra-platoon stability are presented. The most important merit of this method compared to previous works, is that control parameters are independent of eigenvalues of matrix H. Several simulation studies are provided to show the effectiveness of the proposed approaches.

Keywords

Complex eigenvalues CTCR decoupling inter-platoon intra-platoon internal stability string stability time delay

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