非平衡拓扑和随机干扰情形下多自主体系统的趋同条件

研究了具有一般有向通信拓扑和高斯通信噪声的多自主体系统的趋同条件.这里所研究的有向拓扑不仅包含有向平衡图,而且包含非平衡图,后者是本文的重点.我们利用马氏链的结果得到了一个网络节点的互通类;通过对噪声影响的细化,给出了不同噪声情形下系统趋同条件:(1)对互通类的自主体获取信息受到噪声干扰情形,给出了系统均方趋同的充要条件,并证明该条件也保证以概率1 趋同;(2)对互通类的自主体获取信息未受到噪声干扰但其余自主体获取信息受到干扰情形,给出了系统均方趋同的充分条件,并证明该条件在一定意义下也是必要的;(3)对整个系统无噪声情形,给出了系统趋同的充要条件.

CONSENSUS CONDITIONS OF MULTI-AGENT SYSTEMS WITH UNBALANCED TOPOLOGY AND STOCHASTIC DISTURBANCES

Consensus conditions of multi-agent systems with general directed communication topology and Guassian communication noises are investigated. Here the topology includes not only the balanced graphes but also unbalanced graphes, and the latter is the main concern of this paper. By using the results of Markov chains, a communication class of network nodes is given. By considering the influence of the noises, the consensus conditions are provided: (1) for the case where the information received by some agents in the communication class corrupted by noises, a sufficient and necessary condition of mean square consensus is given. It is shown that this condition can also ensure almost sure consensus. (2) For the case where no information received by the agents in the communication class is corrupted, but the information received by some agentsoutside of the communication class is corrupted, a sufficient condition of mean square consensus is obtained, which is shown to be necessary in some sense. (3) For the case without noise, a sufficient and necessary condition of consensus is presented.