标题： 大型车辆编队的分布式控制：稳定性裕度和对外部干扰的敏感性 显示英文标题

标题： Decentralized control of large vehicular formations: stability margin and sensitivity to external disturbances

摘要： 我们研究大规模车辆编队的稳定性和鲁棒性，其中每个车辆被建模为一个双积分器。 考虑了两种类型的信息图：有向树和无向图。 我们证明了对于线性以及一类非线性控制器，具有任意数量车辆的编队是稳定的。 在使用线性控制的情况下，我们提供了稳定性裕度和对外部干扰（H-无穷范数）敏感性的定量尺度定律，相对于编队中的车辆数量$N$。 结果显示，具有有向树图的编队实现了与大小无关的稳定性裕度，但初始误差的代数增长较高。 在无向图的情况下，稳定性裕度随着至少$O(1/N)$而衰减到 0。 此外，我们表明有向树图对外部干扰的敏感性在$k$中呈几何增长，其中$k <= N$是有向树的代数数量，而无向图的敏感性仅在$N$中呈二次增长。 特别是对于一维车辆队列，我们得到了从干扰到位置误差的传递函数的 H-无穷范数的精确公式。 结果显示，对于前车跟随架构，H-无穷范数按$O(\alpha^N) (\alpha>1)$缩放，而对于对称双向架构，仅按$O(N^3)$缩放。 对于一类非线性控制器，数值仿真表明，具有有向树图的编队由于初始误差引起的瞬态响应和对外部干扰的敏感性得到了显著改善。 然而，通过使用所考虑的非线性控制器，对无向图的编队几乎没有改进。 显示英文摘要

摘要： We study the stability and robustness of large-scale vehicular formations, in which each vehicle is modeled as a double-integrator. Two types of information graphs are considered: directed trees and undirected graphs. We prove stability of the formation with arbitrary number of vehicles for linear as well as a class of nonlinear controllers. In the case of linear control, we provide quantitative scaling laws of the stability margin and sensitivity to external disturbances (H-infinity norm) with respect to the number of vehicles $N$ in the formation. It is shown that the formation with directed tree graph achieves size-independent stability margin but suffers from high algebraic growth of initial errors. The stability margin in case of the undirected graph decays to 0 as at least $O(1/N)$. In addition, we show that the sensitivity to external disturbances in directed tree graphs is geometric in $k$ where $k <= N$ is the number of generations of the directed tree, while that of the undirected graph is only quadratic in $N$. In particular, for 1-D vehicular platoons, we obtain precise formulae for the H-infinity norm of the transfer function from the disturbances to the position errors. It is shown that the H-infinity norm scales as $O(\alpha^N) (\alpha>1)$ for predecessor-following architecture, but only as $O(N^3)$ for symmetric bidirectional architectures. For a class of nonlinear controllers, numerical simulations show that the transient response due to initial errors and sensitivity to external disturbances are improved considerably for the formation with directed tree graphs. However, by using the nonlinear controller considered, little improvement can be made for that with undirected graphs.