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In this work, we study the problem of unconstrained convex optimization in a fully distributed multiagent setting, which includes asynchronous computation and lossy communication. In particular, we extend a recently proposed algorithm named Newton–Raphson consensus by integrating it with a broadcast-based average consensus algorithm, which is robust to packet losses. We show via the separation of time-scale principle that under mild conditions (i.e., persistency of the agents activation and bounded consecutive communication failures), the proposed algorithm is provably locally exponentially stable with respect to the optimal global solution. Finally, we complement the theoretical analysis with numerical simulations and comparisons based on real datasets. [ABSTRACT FROM AUTHOR]

A broad family of randomized clock synchronization protocols based on a second order consensus algorithm is proposed. Under mild conditions on the graph connectivity, it is proved that the parameters of the algorithm can always be tuned in such a way that the clock synchronization is achieved in the probabilistic mean—square sense. This family of algorithms contains, as particular cases, several known approaches which range from distributed asynchronous to hierarchical synchronous protocols. This is illustrated by specializing the algorithm for the well-known broadcast and gossip scenarios in wireless communications, and for the standard hierarchical protocol used in the context of wired communications in data networks. In these cases, we show how the feasible range for the algorithm parameters can be explicitly computed. Finally, the performance of this strategy is validated by actual implementation in a real testbed and by numerical simulations. [ABSTRACT FROM PUBLISHER]

In this paper a distributed algorithm for clock synchronization is proposed. This algorithm is based on an extension of the linear consensus algorithm which is able to synchronize a family of identical double integrators. Since in reality the various clocks may have different drifts, the algorithm needs to be designed in such a way that it works correctly also in case of heterogeneous double integrators. We start by reviewing an unrealistic synchronous implementation of the clock synchronization algorithm, that has been recently proposed in the context of noisy double integrators. The main contribution of this paper is to propose a realistic pseudo-synchronous implementation of this algorithm. This pseudo-synchronous algorithm is shown to be a perturbation of the synchronous one and so, through arguments related to the center manifold theorem, it is proved to be locally convergent under the assumption of absence of process noise, measurement noise and propagation delays. However, through numerical simulations, the performance of this algorithm is evaluated also in the case the communication delays are not negligible, the clock drifts are time-varying and the communication channels are unreliable. Moreover, again through numerical simulations, the strategy we propose in this paper is compared with other fully distributed strategies recently proposed in the literature. While being slightly slower to reach the asymptotic synchronization, our strategy seems to significantly outperform the other strategies in terms of robustness to process and measurement noises and time-varying clock drifts. [ABSTRACT FROM AUTHOR]

In this technical note, we present a novel synchronization protocol to synchronize a network of controlled discrete-time double integrators which are nonidentical, with unknown model parameters and subject to additive measurement and process noise. This framework is motivated by the typical problem of synchronizing a network of clocks whose speeds are nonidentical and are subject to variations. This synchronization protocol is formally studied in its synchronous implementation. In particular, we provide a completely distributed strategy that guarantees convergence for any undirected connected communication graph and we also propose an optimal design strategy when the underlaying communication graph is known. Moreover, this protocol can be readily used to study the effect of noise and external disturbances on the steady-state performance. Finally, some simulations including also randomized implementation of the proposed algorithm are presented. [ABSTRACT FROM AUTHOR]