Geodesic
Variations of $v$-change of time in an~optimal control problem with state and mixed constraints
Izvestiya. Mathematics , Tome 87 (2023) no. 4, pp. 726-767

Voir la notice de l'article provenant de la source Math-Net.Ru

For a general optimal control problem with state and regular mixed constraints we propose a proof of the maximum principle based on the so-called $v$-change of time variable $t \mapsto \tau$, under which the original time becomes an additional state variable subject to the equation $dt/d\tau = v(\tau)$, while the additional control variable $v(\tau)\geqslant 0$ is piecewise constant, and its values become arguments of the new problem.
Keywords: state and mixed constraints, positively linearly independent vectors, $v$-change of time, stationarity conditions, Lagrange multipliers, functional on $L_\infty$, weak* compactness, maximum principle.
Mots-clés : Lebesgue–Stieltjes measure 
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     author = {A. V. Dmitruk},
     title = {Variations of $v$-change of time in an~optimal control problem with state and mixed constraints},
     journal = {Izvestiya. Mathematics },
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     publisher = {mathdoc},
     volume = {87},
     number = {4},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2023_87_4_a2/}
}
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A. V. Dmitruk. Variations of $v$-change of time in an~optimal control problem with state and mixed constraints. Izvestiya. Mathematics , Tome 87 (2023) no. 4, pp. 726-767. http://geodesic.mathdoc.fr/item/IM2_2023_87_4_a2/