Abstract:
We study the properties of the trajectories of a differential inclusion with unbounded measurable–pseudo-Lipschitz right-hand side that takes values in a separable Banach space and consider the problem of minimizing a functional over the set of trajectories of such a differential inclusion on an interval. We obtain necessary optimality conditions in the form of Euler–Lagrange differential inclusions for a problem with free right end.
Citation:
E. S. Polovinkin, “Differential inclusions with unbounded right-hand side and necessary optimality conditions”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 291, MAIK Nauka/Interperiodica, Moscow, 2015, 249–265; Proc. Steklov Inst. Math., 291 (2015), 237–252
\Bibitem{Pol15}
\by E.~S.~Polovinkin
\paper Differential inclusions with unbounded right-hand side and necessary optimality conditions
\inbook Optimal control
\bookinfo Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2015
\vol 291
\pages 249--265
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3684}
\crossref{https://doi.org/10.1134/S0371968515040196}
\elib{https://elibrary.ru/item.asp?id=24776676}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 291
\pages 237--252
\crossref{https://doi.org/10.1134/S0081543815080192}
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Linking options:
https://www.mathnet.ru/eng/tm3684
https://doi.org/10.1134/S0371968515040196
https://www.mathnet.ru/eng/tm/v291/p249
This publication is cited in the following 5 articles:
Dolgopolik M., “Constrained Nonsmooth Problems of the Calculus of Variations”, ESAIM-Control OPtim. Calc. Var., 27 (2021), 79
Polovinkin E.S., “On Continuous Variations of Trajectories of Differential Inclusion With Unbounded Right-Hand Side”, Optimization, 69:4 (2020), 703–728
E. S. Polovinkin, “O nepreryvnoi zavisimosti traektorii differentsialnogo vklyucheniya ot nachalnykh priblizhenii”, Tr. IMM UrO RAN, 25, no. 1, 2019, 174–195
E. S. Polovinkin, “Pontryagin's Direct Method for Optimization Problems with Differential Inclusion”, Proc. Steklov Inst. Math., 304 (2019), 241–256
E. S. Polovinkin, “Necessary optimality conditions for the Mayer problem with unbounded differential inclusion”, IFAC PAPERSONLINE, 51:32 (2018), 521–524
Citation in format AMSBIB
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