Abstract
The subject of this note is the algorithm of evolution of a point set on the plane devised in [5], which drives the whole set to a certain regular configuration. Generalizations of the algorithm are proposed and analyzed, certain new properties are studied, connections to formation control methods is discussed, and new simpler algorithms of this sort are proposed.
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Amosov, A.A., Dubinskii, Yu.A., and Kopchenova, N.V., Vychislitel’nye metody dlya inzhenerov (Numerical Methods for Engineers), Moscow: Vysshaya Shkola, 2008.
Golub, G.H. and van Loan, C.F., Matrix Computations, Baltimore: Johns Hopkins Univ. Press, 1989, 2nd ed. Translated under the title Matrichnye vychisleniya, Moscow: Mir, 1989.
Tyrtyshnikov, E.E., Metody chislennogo analiza (Methods of Numerical Analysis), Moscow: Akademiya, 2007.
Petrikevich, Ya.I., Linear Algorithms for Control of Geometrical Allocation of Agents in Multi-Agent Systems, Upravl. Bol’shimi Sist., 2010, vol. 30.1, pp. 665–680.
Elmachtoub, A.N. and van Loan, C.F., From Random Polygon to Ellipse: An Eigenanalysis, SIAM Review, 2010, vol. 52, no. 1, pp. 151–170.
Shoham, Y. and Leyton-Brown, K., Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge: Cambridge Univ. Press, 2009.
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Original Russian Text © P.S. Shcherbakov, 2010, published in Upravlenie Bol’shimi Sistemami, 2010, No. 30.1, pp. 681–696.
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Shcherbakov, P.S. Formation control: The van loan scheme and other algorithms. Autom Remote Control 72, 2210–2219 (2011). https://doi.org/10.1134/S0005117911100195
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DOI: https://doi.org/10.1134/S0005117911100195