Recognition of additively weighted Voronoi diagrams and weighted Delaunay decompositions

Ngoc Anh Nguyen 1, 2 Sorin Olaru 1, 2, 3 Pedro Rodriguez-Ayerbe 1, 2
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : Additively weighted Voronoi diagram and weighted Delaunay decomposition are a generalization of Voronoi diagram and Delaunay triangulation, respectively. They have received much attention due to their relevance in many domains see [1], [2], [3]. In particular, their interest in control theory has been recently shown in [4], [5] to solve inverse parametric linear/quadratic programming problem. This paper elaborates on the identification of suitable sites and weights of such particular partitions via two algorithms. It will be shown that these algorithms require solving a bi-linear programming problem
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Ngoc Anh Nguyen, Sorin Olaru, Pedro Rodriguez-Ayerbe. Recognition of additively weighted Voronoi diagrams and weighted Delaunay decompositions. 14th annual European Control Conference - ECC 2015, Jul 2015, LINZ, Austria. pp.328-333, ⟨10.1109/ECC.2015.7330565⟩. ⟨hal-01259935⟩



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