具有随机丢包的网络化多自主体系统的一致性

Consensus Problem of Networked Multi-agent Systems with Stochastic Packet Losses

研究具有随机丢包的网络化多自主体系统的均方一致性问题,其中不同自主体间的通信通道具有相同的丢包情况并且均服从马尔可夫(Markov)分布。首先,利用系统变换和迭代方法,得到了系统达到均方一致的一个初等充要条件。然后,利用矩阵理论和图论知识,如果拓扑图含有有向生成树,则可以将系统的均方一致性转化成一个线性Markov跳变系统的均方稳定性,并且可以建立线性矩阵不等式形式的均方可镇定准则。最后,通过相应的仿真实例说明了所得结论的可行性。

This paper studied the mean - square consensus problem of networked multi - agent systems with pack- et dropouts, where the communication link failures among all the agents were assumed to be synchronous and the packet - loss process was driven by a Markov chain. First, using the system transformation method and the iterative approach, a preliminary necessary and sufficient condition concerning the mean - square consensus of multi - agent systems was presented. Then, by matrix theory and graph theory, the mean - square consensus of multi - agent sys- tems with a topology having a spanning tree was converted into the mean - square stability of a Markovian jump linear system, whose related mean - square stabilizability criteria was established in the form of linear matrix inequalities （LMIs）. Finally, numerical examples were given to illustrate our results.