相关随机拓扑中的一致性：有限时域上的权
Consensus in Correlated Random Topologies: Weights for Finite Time Horizon
摘要：
我们考虑有限时间范围内的共识算法的权重设计问题。我们假设底层网络是随机的，其中链路以一定的概率在每次迭代中失效，并且链路失效可以是空间相关的。我们制定了一个家庭的重量设计标准（目标函数），最小化n，n = 1，.，描述均方一致性误差动态的矩阵的N个（N个可能中的）最大（最慢）特征值。我们表明，目标函数是凸的，因此，全局最优的权重（相对于设计标准）可以有效地获得。在大规模、稀疏随机网络上的数值例子表明：1）根据我们的标准获得的权重比文献中的选择导致更快的收敛; 2）对应于不同n的不同设计标准表现出非常有趣的权衡：更快的瞬态性能导致更慢的长时间运行性能，反之亦然。因此，n是一个有价值的自由度，并且可以针对给定的时间范围适当地选择。
英文摘要：
We consider the weight design problem for the consensus algorithm under a finite time horizon. We assume that the underlying network is random where the links fail at each iteration with certain probability and the link failures can be spatially correlated. We formulate a family of weight design criteria (objective functions) that minimize n, n = 1,...,N (out of N possible) largest (slowest) eigenvalues of the matrix that describes the mean squared consensus error dynamics. We show that the objective functions are convex; hence, globally optimal weights (with respect to the design criteria) can be efficiently obtained. Numerical examples on large scale, sparse random networks with spatially correlated link failures show that: 1) weights obtained according to our criteria lead to significantly faster convergence than the choices available in the literature; 2) different design criteria that corresponds to different n, exhibits very interesting tradeoffs: faster transient performance leads to slower long time run performance and vice versa. Thus, n is a valuable degree of freedom and can be appropriately selected for the given time horizon.
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