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Multi-agent coordination algorithms with randomized interactions have seen use in a variety of settings in the multi-agent systems literature. In some cases, these algorithms can be random by design, as in a gossip-like algorithm, and in other cases they are random due to external factors, as in the case of intermittent communications. Targeting both of these scenarios, we present novel convergence...
We consider the consensus for multiple double-integrator agents systems in a general framework that the position and velocity interactions among agents are modeled by independent graphs. Different algorithms are proposed and analyzed for various different settings, including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies, as well...
We take a structural approach to the problem of designing the edge weights in an undirected graph subject to an upper bound on their total, so as to maximize the algebraic connectivity. Specifically, we first characterize the eigenvector(s) associated with the algebraic connectivity at the optimum, using optimization machinery together with eigenvalue sensitivity notions. Using these characterizations,...
Expanders have many applications in Computer Science. It is known that random d-regular graphs are very efficient expanders, almost surely. However, checking whether a particular graph is a good expander is co-NP-complete. We show that the second eigenvalue of d-regular graphs, λ2, is concentrated in an interval of width O(√d) around its mean, and that its mean is O(d3/4). The result holds under various...
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