标题： 基于图论的k-最近邻车辆编队鲁棒性方法 显示英文标题

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

摘要： 我们考虑一种图论方法来分析车辆编队的性能和鲁棒性，其中每个车辆与其$k$个最近的邻居进行通信。 特别是，我们通过节点度数和（接地的）拉普拉斯矩阵特征值等图论概念来量化编队的稳定裕度、对扰动的鲁棒性（以系统$\mathcal{H}_{\infty}$范数表示）以及最大延迟容忍度。 我们的结果表明，在时间延迟的鲁棒性和扰动的鲁棒性之间存在权衡。 在此方向上，分析了第一阶动力学（参考速度跟踪）和第二阶动力学（控制车距）。 理论贡献通过仿真结果得到了验证。 显示英文摘要

摘要： 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.