Li Mengling, Deng Feiqi
School of Mathematics and Big Data, Foshan University, Foshan 528000, PR China.
School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, PR China.
ISA Trans. 2021 Oct;116:113-120. doi: 10.1016/j.isatra.2021.01.034. Epub 2021 Jan 20.
This paper focuses on the mean square cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noise via pinning control technique. Network topology can take weaker conditions in each cluster but an extra balanced condition is also needed. A time-varying control gain will be introduced to eliminate the effect of stochastic noise. For the case of fixed topology, if the induced digraph of each cluster has a directed spanning tree, the sufficient conditions for the mean square cluster consensus can be obtained. For the case of Markovian switching topologies, if the induced digraph of union of the Laplacian matrix of each mode has a directed spanning tree, the mean square cluster consensus conclusion can be derived. Particularly, if the elements of transition probability of Markov chain are partly unknown, we can also obtain the same conclusion under the same conditions. Finally, two examples are given to illustrate our results.
本文通过牵制控制技术研究具有马尔可夫切换拓扑和通信噪声的非线性多智能体系统的均方簇一致性。网络拓扑在每个簇中可以采用较弱的条件，但还需要一个额外的平衡条件。将引入一个时变控制增益来消除随机噪声的影响。对于固定拓扑的情况，如果每个簇的诱导有向图具有有向生成树，则可以得到均方簇一致性的充分条件。对于马尔可夫切换拓扑的情况，如果每个模式的拉普拉斯矩阵的并集的诱导有向图具有有向生成树，则可以得出均方簇一致性结论。特别地，如果马尔可夫链转移概率的元素部分未知，在相同条件下我们也可以得到相同的结论。最后，给出两个例子来说明我们的结果。
