On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian

By Yoonsoo Kim, Mehran Mesbahi. 2006

653 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Molecular Biology

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In Molecular Biology

Citations in the corpus

An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination (2012, methodology): “In cont rast to [155], [230], where the systems are assumed to have single-integrator kin ematics, optimization of the convergence speed for double-integrator dynamics was considered in [ 231], where the convergence speed is defined in a similar way to theλ2(L) for the case with single-integrator ki”
Distributed Control of Robotic Networks (2009, background): “Boyd [2006], de Gennaro and Jadbabaie [2006] consider convex constraints, while Kim and Mesbahi [2006] deal with a class of nonconvex constraints.”
Distributed robust finite-time nonlinear consensus protocols for multi-agent systems (2016, background): “…and demonstrated that the algebraic connectivity of a interaction graph, i.e., the second smallest eigenvalue of the graph Laplacian, qualiﬁed the convergence rate, which motivated some researchers to seek proper interaction topology with larger algebraic connectivity (Kim & Mesbahi, 2006).”
Coordination in multiagent systems and Laplacian spectra of digraphs (2009, background): “It is noteworthy that in case of undirected graphs, the problem of the best convergence is connected [29] with the maximization of the algebraic connectivity (the second smallest eigenvalue of the Laplacian matrix already mentioned in Section 3) of the communication graph.”
Spectral radius minimization for optimal average consensus and output feedback stabilization (2009, neutral): “These applications include consensus with statically or dynamically changing information-exchange topologies [14], highfrequency channel noise [15], corrupted measurement data [18], network link failures [6], or state-dependent graph settings [11].”
A Class of Bounded Distributed Control Strategies for Connectivity Preservation in Multi-Agent Systems (2010, background): “In [11] and [12], the problem is tackled by maximizing the second largest eigenvalue of the state-dependent Laplacian of the network graph.”
Distributed connectivity control of mobile networks (2007, background): “In [4], the problem of maximizing the second smallest eigenvalue of a graph Laplacian matrix is investigated, while a decentralized approach to this problem that makes use of a supergradient algorithm and distributed eigenvector computation is considered in [5].”
An Overview of Recent Advances in Fixed-Time Cooperative Control of Multiagent Systems (2018, background): “To increase the convergence rate, some investigations are carried out by the proper design of the interaction graph among agents [9].”
Distributed Optimization for Multiagent Systems: An Edge-Based Fixed-Time Consensus Approach (2019, background): “Some results are obtained to increase the algebraic connectivity by the proper design of an interaction graph [18].”
Decentralized Control of Connectivity for Multi-Agent Systems (2006, methodology): “The optimization ofλ2 has been performed by the SDP [11], but this method is not decentralized.”
Graph-theoretic connectivity control of mobile robot networks (2011, methodology): “Since λ2(L) is a function of the network’s structure via the Laplacian matrix, connectivity algorithms that relied on it were initially centralized [41].”
Cooperative Control of Multiple Nonholonomic Mobile Agents (2008, methodology): “However, increasing the number of interconnections does not necessarily imply a larger value of . Under the same topology of the communication digraph , different weights may lead to different . One can choose the weights to maximize using the methods in [ 39 ].”
Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics (2018, background): “This motivated Kim and Mesbahi [5] to seek proper interaction topology with larger algebraic connectivity.”