Abstract—The paper studies average consensus with random topologies (intermittent links) and noisy channels. Consensus with noise in the network links leads to the bias-variance dilemma—running consensus for long reduces the bias of the final average estimate but increases its variance. We present two different compromises to this tradeoff: the algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition (slowly decaying to zero;) and the algorithm where the weights are constant but consensus is run for a fixed number of iterations, then it is restarted and rerun for a total of runs, and at the end averages the final states of the runs (Monte Carlo averaging). We use controlled Markov processes and stochastic approximation arguments to prove almost sure convergence of to a finite consensus limit and compute explicitly the mean square error (mse) (variance) of the consensus limit. We show that represents the best of both worlds—zero bias and low variance—at the cost of a slow convergence rate; rescaling the weights balances the variance versus the rate of bias reduction (convergence rate). In contrast, , because of its constant weights, converges fast but presents a different bias-variance tradeoff. For the same number of iterations, shorter runs (smaller) lead to high bias but smaller variance (larger number of runs to average over.) For a static nonrandom network with Gaussian noise, we compute the optimal gain for to reach in the shortest number of iterations, with high probability (1), ()-consensus ( residual bias). Our results hold under fairly general assumptions on the random link failures and communication noise. Index Terms—Additive noise, consensus, sensor networks, stochastic approximation, random topology. I.

We consider the problem of cooperatively minimizing the sum of convex functions, where the functions represent local objective functions of the agents. We assume that each agent has information about his local function, and communicate with the other agents over a time-varying network topology. For this problem, we propose a distributed subgradient method that uses averaging algorithms for locally sharing information among the agents. In contrast to previous works on multi-agent optimization that make worst-case assumptions about the connectivity of the agents (such as bounded communication intervals between nodes), we assume that links fail according to a given stochastic process. Under the assumption that the link failures are independent and identically distributed over time (possibly correlated across links), we provide almost sure convergence results for our subgradient algorithm.

This paper addresses task assignment in the coordination of a fleet of unmanned vehicles by presenting two decentralized algorithms: consensus-based auction algorithm (CBAA) and its generalization to the multi-assignment problem, consensus-based bundle algorithm (CBBA). These algorithms utilize a market-based decision strategy as the mechanism for decentralized task selection, and use a consensus routine based on local communication as the conflict resolution mechanism by achieving agreement on the winning bid values. The conflict resolution process of CBBA is further enhanced to address the dependency of the score value on the previously selected tasks in the multi-assignment setting. This work shows that the proposed algorithms, under reasonable assumptions on the scoring scheme and network connectivity, guarantee convergence to a conflict-free assignment. Also, the converged solutions are shown to guarantee 50 % optimality in the worst-case and to exhibit provably good performance on average. Moreover, the proposed algorithms produce a feasible assignment even in the presence of inconsistency in situational awareness across the fleet, and even when the score functions varies with time in some standard manner. Numerical experiments verify quick convergence and good performance of the presented methods for both static and dynamic assignment problems. I.

In this paper we analyze randomized coordination control strategies for the rendezvous problem of multiple agents with unknown initial positions. The performance of these control strategies is measured in terms of three metrics: average relative agents’ distance, total input energy consumption, and number of packets per unit time that each agent can receive from the other agents. By considering an LQ-like performance index, we show that a-priori knowledge about the first and second order statistics of agents’ initial position can greatly improve performance as compared to rendezvous control strategies based only on relative distance feedback. Moreover, we show that randomly switching communication topologies, as compared to static communication topologies, require very little information exchange to achieve high performance even when the number of agents grows very large.

Abstract—In the past decade, complex networks have attracted much attention from various fields of sciences and engineering. Synchronization is a typical collective behavior of complex networks that has been extensively investigated in recent years. To reveal the dynamical mechanism of synchronization in complex networks with time delays, a general complex dynamical network with delayed nodes is further studied. Based on a suitable model, we investigate the adaptive feedback synchronization and obtain several novel criteria for globally exponentially asymptotic synchronization. In particular, our hypotheses and the proposed adaptive controllers for network synchronization are very simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria. Index Terms—Adaptive feedback synchronization, complex networks, delayed nodes. I.

Abstract — We consider the problem of cooperatively minimizing the sum of convex functions, where the functions represent local objective functions of the agents. We assume that each agent has information about his local function, and communicate with the other agents over a time-varying network topology. For this problem, we propose a distributed subgradient method that uses averaging algorithms for locally sharing information among the agents. In contrast to previous works that make worst-case assumptions about the connectivity of the agents (such as bounded communication intervals between nodes), we assume that links fail according to a given stochastic process. Under the assumption that the link failures are independent and identically distributed over time (possibly correlated across links), we provide convergence results and convergence rate estimates for our subgradient algorithm. I.

This work addresses the issue of network connectivity for a team of heterogeneous agents operating in a dynamic environment. The Consensus-Based Bundle Algorithm (CBBA), a distributed task allocation framework previously developed by the authors and their colleagues, is introduced as a methodology for complex mission planning, and extensions are proposed to address limited communication environments. In particular, CBBA with Relays leverages information available through already existing consensus phases to predict the network topology at select times and creates relay tasks to strengthen the connectivity of the network. By employing underutilized resources, the presented approach improves network connectivity without limiting the scope of the active agents, thus improving mission performance. I.

The thesis develops methodology and algorithms to study distributed inference problems in large scale networked systems. Typical examples that fall under the scope of this study include distributed detection, distributed field reconstruction (estimation) arising in wireless sensor network (WSN) applications, and filtering in networked dynamical (cyberphysical) systems. The systems in question operate in random environments and are constrained in terms of resources, like communication bandwidth or power. Due to the inherent randomness in sensor deployment or field sampling, often there is no center coordinating the network activity. The nodes (sensors or dynamical agents) need to collaborate with each other through local information exchange to achieve desired global network behavior. One aspect of our work involves the development of robust distributed algorithms for collaborative information processing in these networks. We study the performance of these distributed schemes in terms of their robustness to communication failures, external stochastic perturbations, and convergence to the corresponding centralized counterparts. The other aspect of the work

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On some properties of contracting matrices