Graph Theoretic Approach to the Robustness of $k$ -Nearest Neighbor Vehicle Platoons

We consider a graph-theoretic approach to the performance and robustness of a platoon of vehicles, in which each vehicle communicates with its k-nearest neighbors. In particular, we quantify the platoon's stability margin, robustness to disturbances (in terms of system H∞ norm), and maximum delay tolerance via graph-theoretic notions, such as nodal degrees and (grounded) Laplacian matrix eigenvalues. The results show that there is a trade-off between robustness to time delay and robustness to disturbances. Both lurst-order dynamics (reference velocity tracking) and second-order dynamics (controlling inter-vehicular distance) are analyzed in this direction. Theoretical contributions are conlurmed via simulation results.