Abstract: The finite-time synchronization of complex networks was used to study the finite-time equilibrium problem of stochastic urban bus networks. Due to that the urban bus network was a typical complex network and based on the concept of driving-response systems in complex networks, the global Lyapunov function was indirectly constructed by using graph-theoretic method. The driving system represented the balanced operation of the urban bus network in an ideal state, while the response system represented the actual operation of the urban bus network. Then, the synchronization of driving system and response system was realized in a finite time, which was combined with finite-time control strategy and stability theory. Therefore, in the urban bus network, through appropriate traffic scheduling, the network subjected to random interference could achieve consistency with the operation state of the ideal state (balanced operation) network in a finite time. In other words, the urban bus networks affected by stochastic disturbance could restore the balance operation in finite time. Finally, numerical example was used to verify the validity and feasibility of the theoretical results, in which the Chua system was used as the vertex system and the small-world network was used to describe the urban bus networks.

Key words: traffic and transportation engineering; finite-time synchronization; graph-theoretic method; stochastic perturbation; urban bus networks

摘要： 借助复杂网络的有限时间同步研究随机城市公交网络(公共汽车交通网络)的有限时间平衡问题。由于城市公交网络是典型的复杂网络，所以基于复杂网络中驱动-响应系统概念(驱动系统表示理想状态下平衡运行的城市公交网络，响应系统表示实际运行的城市公交网络)，先用图论方法间接构建全局李雅普诺夫函数。再结合有限时间控制策略和稳定性理论等使得驱动系统和响应系统在有限时间内实现同步。因此在城市公交网络中，通过合适的交通调度，受到随机干扰后的网络可以和理想状态下(平衡运行)的网络的运行状态在有限时间内达到一致。即受到随机干扰的城市公交网络能在有限时间内恢复平衡运行。最后，通过数值算例来验证理论结果的有效性和可行性，用Chua系统作为顶点系统，用小世界网络刻画城市公交网络。

关键词: 交通运输工程; 有限时间同步；图论方法；随机扰动；城市公交网络