具有随机切换拓扑和时滞的离散时间多智能体网络中的一致性与同步
Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays
AI总结：
针对时变拓扑和时滞的多智能体网络，研究一致性算法的稳定性，证明在自环无延迟条件下网络达到一致，在自环有延迟且满足特定整数模式时算法可能同步到周期轨迹。
摘要：
我们分析了具有时变拓扑和时滞的多智能体网络中一致性算法的稳定性。拓扑和时滞被建模为由适应过程诱导，并且相当一般，包括独立同分布拓扑过程、异步一致性算法和马尔可夫跳变切换。在自环无延迟的情况下，我们证明如果有限时间区间内耦合矩阵之和的条件期望对应的图几乎必然具有生成树，则网络对于所有有界延迟达到一致。此外，当自环也有延迟且延迟满足特定整数模式时，我们观察并证明算法可能不会达到一致，而是同步到一条周期轨迹，其周期取决于延迟模式。我们还简要讨论了无自环情况下的动力学。
英文摘要：
We analyze stability of consensus algorithms in networks of multi-agents with time-varying topologies and delays. The topology and delays are modeled as induced by an adapted process and are rather general, including i.i.d.\ topology processes, asynchronous consensus algorithms, and Markovian jumping switching. In case the self-links are instantaneous, we prove that the network reaches consensus for all bounded delays if the graph corresponding to the conditional expectation of the coupling matrix sum across a finite time interval has a spanning tree almost surely. Moreover, when self-links are also delayed and when the delays satisfy certain integer patterns, we observe and prove that the algorithm may not reach consensus but instead synchronize at a periodic trajectory, whose period depends on the delay pattern. We also give a brief discussion on the dynamics in the absence of self-links.
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