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Contemporary Mathematics. Fundamental Directions, 2011, Volume 42, Pages 118–124 (Mi cmfd194)  
This article is cited in 5 scientific papers (total in 5 papers)

The canonical theory of the impulse process optimality

V. A. Dykhtaab, O. N. Samsonyukab

a Institute of System Dynamics and Control Theory, SB RAS, Irkutsk, Russia
b Institute of Mathematics, Economics and Informatics of Irkutsk State University, Irkutsk, Russia
Full-text PDF (139 kB) Citations (5)
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Abstract: The paper is devoted to the development of the canonical theory of the Hamilton–Jacobi optimality for nonlinear dynamical systems with controls of the vector measure type and with trajectories of bounded variation. Infinitesimal conditions of the strong and weak monotonicity of continuous Lyapunov-type functions with respect to the impulsive dynamical system are formulated. Necessary and sufficient conditions of the global optimality for the problem of the optimal impulsive control with general end restrictions are represented. The conditions include the sets of weak and strong monotone Lyapunov-type functions and are based on the reduction of the original problem of the optimal impulsive control a finite-dimensional optimization problem on an estimated set of connectable points.
English version:
Journal of Mathematical Sciences, 2014, Volume 199, Issue 6, Pages 646–653
DOI: https://doi.org/10.1007/s10958-014-1891-2
Bibliographic databases:
Document Type: Article
UDC: 517.977.5
Language: Russian
Citation: V. A. Dykhta, O. N. Samsonyuk, “The canonical theory of the impulse process optimality”, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), CMFD, 42, PFUR, M., 2011, 118–124; Journal of Mathematical Sciences, 199:6 (2014), 646–653
Citation in format AMSBIB
\Bibitem{DykSam11}
\by V.~A.~Dykhta, O.~N.~Samsonyuk
\paper The canonical theory of the impulse process optimality
\inbook Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3--7, 2009)
\serial CMFD
\yr 2011
\vol 42
\pages 118--124
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd194}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3013832}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 199
\issue 6
\pages 646--653
\crossref{https://doi.org/10.1007/s10958-014-1891-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902841741}
Linking options:
  • https://www.mathnet.ru/eng/cmfd194
  • https://www.mathnet.ru/eng/cmfd/v42/p118
    • This publication is cited in the following 5 articles:
    1. Rashad Mammadov, Sardar Gasimov, Sevinj Karimova, Ibrahim Abbasov, “Approximate Solution of Optimal Pulse Control Problem Associated with the Heat Conduction Process”, Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences., 77:5-6 (2023), 263  crossref
    2. Olga Samsonyuk, Stepan Sorokin, 2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB), 2020, 1  crossref
    3. O. N. Samsonyuk, “Prilozheniya funktsii tipa Lyapunova k zadacham optimizatsii v impulsnykh upravlyaemykh sistemakh”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 14 (2015), 64–81  mathnet
    4. O. N. Samsonyuk, “Funktsii tipa Lyapunova dlya nelineinykh impulsnykh upravlyaemykh sistem”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 7 (2014), 104–123  mathnet
    5. 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  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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