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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 271, Pages 93–110 (Mi tm3238)  
This article is cited in 6 scientific papers (total in 6 papers)

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
Full-text PDF (275 kB) Citations (6)
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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.
Received in February 2010
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 271, Pages 86–102
DOI: https://doi.org/10.1134/S0081543810040085
Bibliographic databases:
Document Type: Article
UDC: 517.977.5
Language: Russian
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, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 93–110; Proc. Steklov Inst. Math., 271 (2010), 86–102
Citation in format AMSBIB
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\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
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\vol 271
\pages 93--110
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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