Achieving robust average consensus over wireless networks

Achieving Robust Average Consensus Over Lossy Wireless Networks

“…Although it is possible to compute the exponential rate of convergence to the network average, it does not lead to insightful closed-form expressions in the general case [20], [21]. The rate of convergence could be bounded solving an eigenvalue problem: however, the computation of such eigenvalues is still generally difficult, unless the scenario is restricted to some specific topology: an extended study of the convergence rate bounds for circulant and complete topologies can be found in [16]. Moreover, when the update rule is modified with a gain α, the eigenvalue problem becomes even more difficult.…”

“…• α h , the heuristic value for α in (16). To increase readability, the number of iterations required to converge is shown over only two parameters: p and m, because the dependence of the number of iterations required to converge on the size of the network appears to be negligible in comparison with the dependence on the probability of packet loss and the connectivity of the network: for a given probability of packet loss, the simulations lie in an interval smaller than 10% of the displayed result.…”

“…Preliminary and partial versions of some of our contribu-tions have appeared or are about to appear in the proceedings of IEEE conferences, namely the compensation method in [16] and the gain-acceleration in [17]. In this journal version, we not only present these results in revised and consistent form, with more details, but we also include a novel, further corrective step (named asynchronous fallback) which is necessary to preserve the average in the asynchronous implementation (Section IV.B and Section IV.C)…”

Using a linear gain to accelerate average consensus over unreliable networks

“…It is possible to study the convergence properties of the network, subjected to failures, examining the matrix W (k): from the properties of a connected and aperiodic graph, and the stochasticity of the matrix W (k), defined in (8), it is possible to conclude that the network converges almost surely to the average of its agents' initial values, and the convergence speed is related to the eigenvalues of W (k). This compensation method has been studied in [13].…”

“…It is also possible to preserve consensus using a local compensation mechanism, which modifies the weights of the links between the nodes to accomodate the change in the network topology, as in [7]. In [13] we proposed a method to compensate the loss of information and guarantee average consensus and we estimated its convergence speed. In this paper, we propose a weight-modifying compensation strategy over networks with unreliable bidirectional links, to deal specifically with packet collisions.…”