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

Mohammad Pirani; Ehsan Hashemi; John W. Simpson-Porco; Baris Fidan; Amir Khajepour

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arXiv · 1607.01821

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

Mohammad Pirani·Ehsan Hashemi·John W. Simpson-Porco·Baris Fidan·Amir Khajepour

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Abstract

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

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Mohammad Pirani, Ehsan Hashemi, John W. Simpson-Porco, Baris Fidan, Amir Khajepour. 2016-07-06. A Graph Theoretic Approach to the Robustness of k-Nearest Neighbor Vehicle Platoons. https://arxiv.org/abs/1607.01821

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