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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 3, Pages 166–179 (Mi timm1092)  

This article is cited in 6 scientific papers (total in 7 papers)

On a group control problem under obstacle avoidance

A. B. Kurzhanskii

Lomonosov Moscow State University

Abstract: We consider the problem of coordinated goal-oriented target control for a group of control systems that are to realize a joint movement towards a given target set under collision avoidance. The members of the group are obliged to lie within a virtual ellipsoidal container, which performs a reference motion while also avoiding external obstacles specified in advance. We describe a general solution scheme based on decomposing the main problem into auxiliary subproblems, for which we indicate solution methods as well as the necessity of coordinating these solutions at the final stage.

Keywords: group control, flocking, target set, ellipsoidal trajectory, reference motion, collision avoidance, obstacles, coordination.

Full text: PDF file (233 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 291, suppl. 1, 128–142

Bibliographic databases:

UDC: 517.977
Received: 07.07.2014

Citation: A. B. Kurzhanskii, “On a group control problem under obstacle avoidance”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 166–179; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 128–142

Citation in format AMSBIB
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\pages 166--179
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\issue , suppl. 1
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. “Alexander Borisovich Kurzhanski. On the occasion of his 75th birthday”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 1–13  mathnet  crossref  mathscinet  isi
    2. A. B. Kurzhanskii, “Problem of collision avoidance for a group motion with obstacles”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 120–136  mathnet  crossref  mathscinet  isi  elib
    3. A. B. Kurzhanski, A. I. Mesyats, “The Hamiltonian Formalism For Problems of Group Control Under Obstacles”, IFAC-PapersOnLine, 49:18 (2016), 570–575  crossref  mathscinet  isi  scopus
    4. A. Yu. Uteshev, M. V. Goncharova, “Point-to-ellipse and point-to-ellipsoid distance equation analysis”, J. Comput. Appl. Math., 328 (2018), 232–251  crossref  mathscinet  zmath  isi  scopus
    5. A. V. Proskurnikov, A. S. Matveev, “Tsypkin and Jury–Lee criteria for synchronization and stability of discrete-time multiagent systems”, Autom. Remote Control, 79:6 (2018), 1057–1073  mathnet  crossref  isi  elib
    6. A. B. Kurzhanskii, “Hamiltonian formalism in team control problems”, Differ. Equ., 55:4 (2019), 532–540  crossref  isi
    7. N. M. Dmitruk, “Stabilization of coupled linear systems via bounded distributed feedbacks”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 30 (2019), 31–44  mathnet  crossref
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