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Rapid Transitions with Robust Accelerated Delayed Self Reinforcement for Consensus-Based Networks

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Document pages: 15 pages

Abstract: Rapid transitions are important for quick response of consensus-based,multi-agent networks to external stimuli. While high-gain can increase responsespeed, potential instability tends to limit the maximum possible gain, andtherefore, limits the maximum convergence rate to consensus during transitions.Since the update law for multi-agent networks with symmetric graphs can beconsidered as the gradient of its Laplacian-potential function, Nesterov-typeaccelerated-gradient approaches from optimization theory, can further improvethe convergence rate of such networks. An advantage of the accelerated-gradientapproach is that it can be implemented using accelerateddelayed-self-reinforcement (A-DSR), which does not require new information fromthe network nor modifications in the network connectivity. However, theaccelerated-gradient approach is not directly applicable to general directedgraphs since the update law is not the gradient of the Laplacian-potentialfunction. The main contribution of this work is to extend theaccelerated-gradient approach to general directed graph networks, withoutrequiring the graph to be strongly connected. Additionally, while both themomentum term and outdated-feedback term in the accelerated-gradient approachare important in general, it is shown that the momentum term alone issufficient to achieve balanced robustness and rapid transitions withoutoscillations in the dominant mode, for networks whose graph Laplacians havereal spectrum. Simulation results are presented to illustrate the performanceimprovement with the proposed Robust A-DSR of 40 in structural robustness and50 in convergence rate to consensus, when compared to the case without theA-DSR. Moreover, experimental results are presented that show a similar 37 faster convergence with the Robust A-DSR when compared to the case without theA-DSR.

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