标题： 潜在共识的模型 显示英文标题

标题： Models of latent consensus

摘要： 本文研究了在依赖有向图$\Gamma$没有生成树的情况下，多智能体系统达成一致的问题。 我们考虑了一种正则化协议，即引入一个与所有智能体均匀连接的虚拟代理（中心节点）。 该中心节点的存在确保了渐近一致性能够实现。 对于虚拟代理的“蒸发”，它对其他智能体的影响强度消失，这引出了潜在一致性这一概念。 当中心节点的连接是对称时，我们得到了一致性的一个显式表达式，在这种情况下，中心节点对一致性的影响力保持固定。 另一方面，如果中心节点主要受智能体影响，而它对它们的影响趋于零，则一致性可以通过$\Gamma$的拉普拉斯特征投影的列均值向量与系统初始状态向量的标量积来表示。 另一种假设智能体之间存在趋于零的弱均匀背景连接的协议，同样会导致相同的潜在一致性。 显示英文摘要

摘要： The paper studies the problem of achieving consensus in multi-agent systems in the case where the dependency digraph $\Gamma$ has no spanning in-tree. We consider the regularization protocol that amounts to the addition of a dummy agent (hub) uniformly connected to the agents. The presence of such a hub guarantees the achievement of an asymptotic consensus. For the "evaporation" of the dummy agent, the strength of its influences on the other agents vanishes, which leads to the concept of latent consensus. We obtain a closed-form expression for the consensus when the connections of the hub are symmetric, in this case, the impact of the hub upon the consensus remains fixed. On the other hand, if the hub is essentially influenced by the agents, whereas its influence on them tends to zero, then the consensus is expressed by the scalar product of the vector of column means of the Laplacian eigenprojection of $\Gamma$ and the initial state vector of the system. Another protocol, which assumes the presence of vanishingly weak uniform background links between the agents, leads to the same latent consensus.