相关切换拓扑下共识算法的权值优化
Weight Optimization for Consensus Algorithms with Correlated Switching Topology
摘要：
我们在空间相关随机拓扑的共识算法中设计权重。这些问题出现在：1）具有空间相关随机链路故障的网络和2）具有随机平均协议的网络。我们证明了对称和非对称随机图的权优化问题都是凸的。对于对称随机网络，我们选择共识均方误差（MSE）收敛速度作为优化标准，并明确表示此速度作为链接形成概率，链接形成空间相关性和共识权重的函数。我们证明了MSE收敛速度是一个凸的，非光滑的函数的权重，使全局优化的权重为任意的链接形成概率和链接相关结构。我们扩展我们的结果的情况下，非对称随机链接。我们采用的优化标准的均方偏差（MSdev）的节点状态从当前的平均状态。我们证明了MSdev是一个凸函数的权重。仿真结果表明，显着的性能增益与我们的重量设计方法相比，在文献中提供的方法。
英文摘要：
We design the weights in consensus algorithms with spatially correlated random topologies. These arise with: 1) networks with spatially correlated random link failures and 2) networks with randomized averaging protocols. We show that the weight optimization problem is convex for both symmetric and asymmetric random graphs. With symmetric random networks, we choose the consensus mean squared error (MSE) convergence rate as optimization criterion and explicitly express this rate as a function of the link formation probabilities, the link formation spatial correlations, and the consensus weights. We prove that the MSE convergence rate is a convex, nonsmooth function of the weights, enabling global optimization of the weights for arbitrary link formation probabilities and link correlation structures. We extend our results to the case of asymmetric random links. We adopt as optimization criterion the mean squared deviation (MSdev) of the nodes states from the current average state. We prove that MSdev is a convex function of the weights. Simulations show that significant performance gain is achieved with our weight design method when compared with methods available in the literature.
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