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 CMFD, 2011, Volume 42, Pages 118–124 (Mi cmfd194)

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

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.

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English version:
Journal of Mathematical Sciences, 2014, 199:6, 646–653

Bibliographic databases:

UDC: 517.977.5

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://www.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} 

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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, “Prilozheniya funktsii tipa Lyapunova k zadacham optimizatsii v impulsnykh upravlyaemykh sistemakh”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 14 (2015), 64–81
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