Abstract This paper concerns with the mean square scaled consensus for multi-agent systems(MAS) with Markovian switching topologies and communication noises. A time-homogeneous Markov process governs the switching and each topology corresponds to a state of the process. Meanwhile, the communication noises are also considered for practical applications. We introduce a time-varying gain in control protocol which can reduce the effect of communication noises. It is shown that the effect of Markovian switching topologies mainly depends on the union of topologies associated with the positive recurrent states of Markov process. Then necessary and sufficient criteria can be established to guarantee the mean square scaled consensus under the action of distributed protocols. Moreover, the L V operator for semi-Markovian switching topologies case is derived and we can extend our result to the cases that the elements of transition rates matrix are partly unknown and the topological structure is semi-Markovian switching. Finally, an example is conducted to demonstrate the validity of our results.

中文翻译：

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具有切换拓扑和通信噪声的多代理系统的缩放共识

摘要 本文关注具有马尔可夫切换拓扑和通信噪声的多智能体系统（MAS）的均方尺度一致性。时间齐次的马尔可夫过程控制切换，每个拓扑对应于过程的一个状态。同时，在实际应用中也考虑了通信噪声。我们在控制协议中引入了时变增益，可以减少通信噪声的影响。结果表明，马尔可夫转换拓扑的效果主要取决于与马尔可夫过程的正循环状态相关联的拓扑的并集。然后可以建立必要和充分的标准来保证分布式协议作用下的均方尺度共识。而且，导出了半马尔可夫切换拓扑的 LV 算子，我们可以将我们的结果扩展到转换率矩阵的元素部分未知并且拓扑结构是半马尔可夫切换的情况。最后，通过一个例子来证明我们结果的有效性。