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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 4, Pages 287–296 (Mi timm1134)  

This article is cited in 2 scientific papers (total in 2 papers)

Estimates of reachable sets of control systems with nonlinearity and parametric perturbations

T. F. Filippovaab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Yeltsin Ural Federal University

Abstract: We consider techniques of estimating trajectory tubes of nonlinear control systems with uncertainty in the initial data and under the assumption of a quadratic nonlinearity of system state velocities over the states of the system. It is assumed that the uncertain initial states and the admissible controls are constrained by ellipsoidal restrictions. We study problems of sensitivity of reachable sets and of their ellipsoidal estimates to finite-dimensional parameters appearing in the constraints and in the uncertain dynamics of the control system. The results are based on algorithms and techniques of the ellipsoidal estimation theory and on the theory of differential inclusions.

Keywords: reachable set, differential inclusions, ellipsoidal calculus, parameter sensitivity.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, 292, suppl. 1, 67–75

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 25.08.2014

Citation: T. F. Filippova, “Estimates of reachable sets of control systems with nonlinearity and parametric perturbations”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 4, 2014, 287–296; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 67–75

Citation in format AMSBIB
\Bibitem{Fil14}
\by T.~F.~Filippova
\paper Estimates of reachable sets of control systems with nonlinearity and parametric perturbations
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 4
\pages 287--296
\mathnet{http://mi.mathnet.ru/timm1134}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3379290}
\elib{http://elibrary.ru/item.asp?id=22515154}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 292
\issue , suppl. 1
\pages 67--75
\crossref{https://doi.org/10.1134/S0081543816020061}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000376272600006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84971574810}


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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. T. F. Filippova, “Ellipsoidal estimates of reachable sets for control systems with nonlinear terms”, IFAC-PapersOnLine, 50:1 (2017), 15355–15360  crossref  isi  scopus
    2. T. F. Filippova, “The HJB approach and state estimation for control systems with uncertainty”, IFAC-PapersOnLine, 51:13 (2018), 7–12  crossref  isi  scopus
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