Distributed Estimation and Control of Algebraic Connectivity over Random Graphs

In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power iteration method that allows each node to estimate and track the algebraic connectivity of the underlying expected graph. Using results from stochastic approximation theory, we prove that the proposed method converges almost surely (a.s.) to the desired value of connectivity even in the presence of imperfect communication scenarios. The estimation strategy is then used as a basic tool to adapt the power transmitted by each node of a wireless network, in order to maximize the network connectivity in the presence of realistic Medium Access Control (MAC) protocols or simply to drive the connectivity toward a desired target value. Numerical results corroborate our theoretical findings, thus illustrating the main features of the algorithm and its robustness to fluctuations of the network graph due to the presence of random link failures.Comment: To appear in IEEE Transactions on Signal Processin

Network connectivity tracking for a team of unmanned aerial vehicles

Algebraic connectivity is the second-smallest eigenvalue of the Laplacian matrix and can be used as a metric for the robustness and efficiency of a network. This connectivity concept applies to teams of multiple unmanned aerial vehicles (UAVs) performing cooperative tasks, such as arriving at a consensus. As a UAV team completes its mission, it often needs to control the network connectivity. The algebraic connectivity can be controlled by altering edge weights through movement of individual UAVs in the team, or by adding and deleting edges. The addition and deletion problem for algebraic connectivity, however, is NP-hard. The contributions of this work are 1) a comparison of four heuristic methods for modifying algebraic connectivity through the addition and deletion of edges, 2) a rule-based algorithm for tracking a connectivity profile through edge weight modification and the addition and deletion of edges, 3) a new, hybrid method for selecting the best edge to add or remove, 4) a distributed method for estimating the eigenvectors of the Laplacian matrix and selecting the best edge to add or remove for connectivity modification and tracking, and 5) an implementation of the distributed connectivity tracking using a consensus controller and double-integrator dynamics

Analysis of the Effects of Failure and Noise in the Distributed Connectivity Maintenance of a Multi-robot System

To perform cooperative tasks in a decentralized manner, multi-robot systems are often required to communicate with each other. Therefore, maintaining the communication graph connectivity is a fundamental issue when roaming a territory with obstacles. However, when dealing with real-robot systems, several sources of data corruption can appear in the agent interaction. In this paper, the effects of failure and noise in the communication between agents are analyzed upon a connectivity maintenance control strategy. The results show that the connectivity strategy is resilient to the negative effects of such disturbances under realistic settings that consider a bandwidth limit for the control effort. This opens the perspective of applying the connectivity maintenance strategy in adaptive schemes that consider, for instance, autonomous adaptation to constraints other than connectivity itself, e.g. communication efficiency and energy harvesting.Comment: 6 pages, 7 figures, published in CINTI 201

Distributed tracking control of leader-follower multi-agent systems under noisy measurement

In this paper, a distributed tracking control scheme with distributed estimators has been developed for a leader-follower multi-agent system with measurement noises and directed interconnection topology. It is supposed that each follower can only measure relative positions of its neighbors in a noisy environment, including the relative position of the second-order active leader. A neighbor-based tracking protocol together with distributed estimators is designed based on a novel velocity decomposition technique. It is shown that the closed loop tracking control system is stochastically stable in mean square and the estimation errors converge to zero in mean square as well. A simulation example is finally given to illustrate the performance of the proposed control scheme.Comment: 8 Pages, 3 figure