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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 268, Pages 56–63 (Mi tm2863)  
This article is cited in 46 scientific papers (total in 46 papers)

On the control of a flock by a leader

R. W. Brockett

School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
Full-text PDF (205 kB) Citations (46)
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Abstract: The collective and individual behaviors of the elements of a set of identical units are investigated from the point of view of their response to a coordination signal broadcast by a leader. In terms of the model used here, we show that for such systems nonlinearity plays a critical role. A new method for establishing controllability of nonlinear, replicated systems is given. Similarly, stabilization also depends on high order nonlinear effects. For the purpose of stabilization, a distinction between odd order nonlinear terms and even order nonlinear terms plays a role.
Received in June 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 268, Pages 49–57
DOI: https://doi.org/10.1134/S0081543810010050
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: English
Citation: R. W. Brockett, “On the control of a flock by a leader”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 56–63; Proc. Steklov Inst. Math., 268 (2010), 49–57
Citation in format AMSBIB
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\paper On the control of a~flock by a~leader
\inbook Differential equations and topology.~I
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
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\vol 268
\pages 56--63
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 46 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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