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 Tr. Mat. Inst. Steklova, 2010, Volume 271, Pages 93–110 (Mi tm3238)

Hamilton–Jacobi inequalities in control problems for impulsive dynamical systems

V. A. Dykhtaab, O. N. Samsonyukab

a Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia
b Institute of Mathematics, Economics and Information Science, Irkutsk State University, Irkutsk, Russia

Abstract: We propose definitions of strong and weak monotonicity of Lyapunov-type functions for nonlinear impulsive dynamical systems that admit vector measures as controls and have trajectories of bounded variation. We formulate infinitesimal conditions for the strong and weak monotonicity in the form of systems of proximal Hamilton–Jacobi inequalities. As an application of strongly and weakly monotone Lyapunov-type functions, we consider estimates for integral funnels of impulsive systems as well as necessary and sufficient conditions of global optimality corresponding to the approach of the canonical Hamilton–Jacobi theory.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 271, 86–102

Bibliographic databases:

UDC: 517.977.5
Received in February 2010

Citation: V. A. Dykhta, O. N. Samsonyuk, “Hamilton–Jacobi inequalities in control problems for impulsive dynamical systems”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 93–110; Proc. Steklov Inst. Math., 271 (2010), 86–102

Citation in format AMSBIB
\Bibitem{DykSam10} \by V.~A.~Dykhta, O.~N.~Samsonyuk \paper Hamilton--Jacobi inequalities in control problems for impulsive dynamical systems \inbook Differential equations and topology.~II \bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin \serial Tr. Mat. Inst. Steklova \yr 2010 \vol 271 \pages 93--110 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3238} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2841714} \elib{https://elibrary.ru/item.asp?id=15524635} \transl \jour Proc. Steklov Inst. Math. \yr 2010 \vol 271 \pages 86--102 \crossref{https://doi.org/10.1134/S0081543810040085} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000287921200008} \elib{https://elibrary.ru/item.asp?id=16974444} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952216216} 

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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. B. M. Miller, E. Ya. Rubinovich, “Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations”, Autom. Remote Control, 74:12 (2013), 1969–2006
2. O. N. Samsonyuk, “Funktsii tipa Lyapunova dlya nelineinykh impulsnykh upravlyaemykh sistem”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 7 (2014), 104–123
3. O. N. Samsonyuk, “Invariant sets for the nonlinear impulsive control systems”, Autom. Remote Control, 76:3 (2015), 405–418
4. O. N. Samsonyuk, “Prilozheniya funktsii tipa Lyapunova k zadacham optimizatsii v impulsnykh upravlyaemykh sistemakh”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 14 (2015), 64–81
5. Claeys M., Henrion D., Kruzik M., “Semi-definite relaxations for optimal control problems with oscillation and concentration effects”, ESAIM-Control OPtim. Calc. Var., 23:1 (2017), 95–117
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