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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 4, Pages 106–115 (Mi timm1119)  
This article is cited in 2 scientific papers (total in 2 papers)

On elimination of state constraints in the construction of reachable sets

M. I. Gusevab

a Yeltsin Ural Federal University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (288 kB) Citations (2)
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Abstract: The paper is devoted to the problem of approximating reachable sets of a nonlinear control system with state constraints given as a solution set of a nonlinear inequality. A state constraint elimination procedure based on the introduction of an auxiliary constraint-free control system is proposed. The equations of the auxiliary system depend on a small parameter. It is shown that the reachable set of the original system can be approximated in the Hausdorff metric by reachable sets of the auxiliary control system as the small parameter tends to zero. Estimates of the convergence rate are given.
Keywords: reachable set, state constraints, penalty function, approximation, Hausdorff metric.
Received: 05.08.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 292, Issue 1, Pages 115–124
DOI: https://doi.org/10.1134/S0081543816020103
Bibliographic databases:
Document Type: Article
UDC: 517.977.1
Language: Russian
Citation: M. I. Gusev, “On elimination of state constraints in the construction of reachable sets”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 4, 2014, 106–115; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 115–124
Citation in format AMSBIB
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\yr 2014
\vol 20
\issue 4
\pages 106--115
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 292
\issue , suppl. 1
\pages 115--124
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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