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 Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 5, Pages 66–75 (Mi timm609)

Analysis of sufficient optimality conditions with a set of Lyapunov type functions

V. A. Dykhta

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: For the classical optimal control problem with general endpoints constraints new variants of the Krotov–Carathéodory type global optimality conditions and sufficient conditions of the so-called Hamilton–Jacobi canonical optimality theory are proposed and compared. These sufficient optimality conditions are obtained and formulated by using some support set of nonsmooth Lyapunov-type functions, which are strongly monotone with respect to the control dynamic system. It is proved that the sufficient optimality conditions corresponding to the canonical theory are more efficient. Some properties of Lyapunov functions from the support set are investigated.

Keywords: sufficient optimality conditions, Lyapunov functions, Hamilton–Jacobi inequalities, support set.

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Citation: V. A. Dykhta, “Analysis of sufficient optimality conditions with a set of Lyapunov type functions”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 5, 2010, 66–75

Citation in format AMSBIB
\Bibitem{Dyk10} \by V.~A.~Dykhta \paper Analysis of sufficient optimality conditions with a~set of Lyapunov type functions \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2010 \vol 16 \issue 5 \pages 66--75 \mathnet{http://mi.mathnet.ru/timm609} \elib{https://elibrary.ru/item.asp?id=15265833} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. A. Dykhta, S. P. Sorokin, “Positional solutions of Hamilton–Jacobi equations in control problems for discrete-continuous systems”, Autom. Remote Control, 72:6 (2011), 1184–1198
2. V. A. Dykhta, S. P. Sorokin, “Hamilton–Jacobi inequalities and the optimality conditions in the problems of control with common end constraints”, Autom. Remote Control, 72:9 (2011), 1808–1821
3. S. P. Sorokin, “Monotonnye funktsii tipa Lyapunova i usloviya globalnoi optimalnosti dlya zadach upravleniya diskretnymi sistemami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 4:3 (2011), 132–145
4. V. A. Dykhta, “Positional strengthenings of the maximum principle and sufficient optimality conditions”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 43–57
5. V. G. Antonik, V. A. Srochko, “Optimality conditions of the maximum principle type in bilinear control problems”, Comput. Math. Math. Phys., 56:12 (2016), 2023–2034
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