Brief paper: Notes on averaging over acyclic digraphs and discrete coverage control

Authors:
Chunkai Gao;Jorge Cortés;Francesco Bullo
Affiliations:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA;Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA;Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

In this paper we study averaging algorithms and coverage control laws in a unified light. First, we characterize the convergence properties of averaging algorithms over acyclic digraphs with fixed and controlled-switching topology. Second, we introduce and study novel discrete coverage control laws, which are useful in practical implementations of coverage strategies. We characterize the close relationship of the novel discrete control laws with continuous coverage control laws and with averaging algorithms over a class of acyclic digraphs, that we term discrete Voronoi graphs. These results provide a unified framework to model a vast class of distributed optimization problems.