2018/05/07 by Johan Thunberg, Johan Markdahl, Thunberg, Johan +5 · 1 citation
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Distributed Control Multi-Agent Systems #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.1805.02528
This paper introduces a new lifting method for analyzing convergence of\ncontinuous-time distributed synchronization/consensus systems on the unit\nsphere. Points on the d-dimensional unit sphere are lifted to the\n(d+1)-dimensional Euclidean space. The consensus protocol on the unit sphere is\nthe classical one, where agents move toward weighted averages of their\nneighbors in their respective tangent planes. Only local and relative state\ninformation is used. The directed interaction graph topologies are allowed to\nswitch as a function of time. The dynamics of the lifted variables are governed\nby a nonlinear consensus protocol for which the weights contain ratios of the\nnorms of state variables. We generalize previous convergence results for\nhemispheres. For a large class of consensus protocols defined for switching\nuniformly quasi-strongly connected time-varying graphs, we show that the\nconsensus manifold is uniformly asymptotically stable relative to closed balls\ncontained in a hemisphere. Compared to earlier projection based approaches used\nin this context such as the gnomonic projection, which is defined for\nhemispheres only, the lifting method applies globally. With that, the hope is\nthat this method can be useful for future investigations on global convergence.\n