Abstract:
An optimal control problem is investigated for a linear system with fast and slow variables, a convex terminal performance functional depending on the slow variables, and smooth geometric constraints on the control. Sufficient regularity conditions are presented for the asymptotics of a solution of this problem, and a complete asymptotic expansion of the optimal value of the performance functional in powers of a small parameter is constructed.
Citation:
A. R. Danilin, Yu. V. Parysheva, “The asymptotics of the optimal value of the performance functional in a linear optimal control problem in the regular case”, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 2, 2007, 55–65; Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S83–S94
\Bibitem{DanPar07}
\by A.~R.~Danilin, Yu.~V.~Parysheva
\paper The asymptotics of the optimal value of the performance functional in a~linear optimal control problem in the regular case
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2007
\vol 13
\issue 2
\pages 55--65
\mathnet{http://mi.mathnet.ru/timm88}
\elib{https://elibrary.ru/item.asp?id=12040768}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2007
\vol 259
\issue , suppl. 2
\pages S83--S94
\crossref{https://doi.org/10.1134/S0081543807060053}
Linking options:
https://www.mathnet.ru/eng/timm88
https://www.mathnet.ru/eng/timm/v13/i2/p55
This publication is cited in the following 5 articles:
A. R. Danilin, A. A. Shaburov, “Asymptotic expansion of the solution of a singularly perturbed optimal control problem with elliptical control constraints”, Autom. Remote Control, 83:1 (2022), 1–16
A. A. Shaburov, “Asimptoticheskoe razlozhenie resheniya singulyarno vozmuschennoi zadachi optimalnogo upravleniya s gladkimi ogranicheniyami na upravlenie i s integralnym vypuklym kriteriem kachestva,
terminalnaya chast kotorogo zavisit tolko ot medlennykh peremennykh”, Vestnik rossiiskikh universitetov. Matematika, 24:125 (2019), 119–136
“On the asymptotics of the optimal value of the performance functional in a linear optimal control problem”, Differ. Equ., 47:4 (2011), 560–570
Yu. V. Parysheva, “Asimptotika optimalnogo upravleniya v zadache minimizatsii terminalnogo funktsionala na traektoriyakh sistemy s bystrymi i medlennymi peremennymi”, Tr. IMM UrO RAN, 16, no. 2, 2010, 186–198
Danilin A.R., Parysheva Yu.V., “Asymptotics of the optimal cost functional in a linear optimal control problem”, Dokl. Math., 80:1 (2009), 478–481
Citation in format AMSBIB
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