Average-consensus with switched Markovian network links

Decentralized network estimation of the average initial node value is considered here in a variety of stochastic network settings. Each setting assumes the elements of the network communication graph edge set are modeled as a collection of ergodic Markov chains with slowly switching regime and unknown stationary distribution. In this framework an asymptotic average-consensus is obtained by using a ldquodampedrdquo distributive averaging algorithm in conjunction with an adaptive weighting scheme. The weighting scheme is designed to off-set the unknown probabilities of node communication by associating with each transmission a weight that is inversely proportional to the current estimate of the nodes communication probability. It is shown that for suitably connected graphs with balanced edge sets, and in particular any connected undirected edge set, the weighting scheme and averaging algorithm together yield a network consensus that is bounded to within an arbitrary distance of the average initial node value. The asymptotic node value scaled error measured relative to the node steady-state is also characterized by a vanishing diffusion equation with parameters that approach zero only as the nodes approach consensus. Simulations employ the proposed algorithm to demonstrate its proficiency and illustrate our results.