Abstract:
A time-optimal control problem is considered for a linear system with fast and slow variables and smooth geometric constraints on the control. For the optimal time and optimal control, asymptotic expansions in a small parameter at the derivatives in the equations of the system and a small perturbation of the initial conditions are constructed.
Keywords:
optimal control, time-optimal control problem, asymptotic expansion, singular perturbation problems, small parameter.
Citation:
A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a singular perturbation linear problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 63–75; Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S53–S65
\Bibitem{DanKov10}
\by A.~R.~Danilin, O.~O.~Kovrizhnykh
\paper Asymptotics of the optimal time in a~singular perturbation linear problem
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 1
\pages 63--75
\mathnet{http://mi.mathnet.ru/timm529}
\elib{https://elibrary.ru/item.asp?id=13072991}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 271
\issue , suppl. 1
\pages S53--S65
\crossref{https://doi.org/10.1134/S0081543810070059}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000284889500005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79953246479}
Linking options:
https://www.mathnet.ru/eng/timm529
https://www.mathnet.ru/eng/timm/v16/i1/p63
This publication is cited in the following 6 articles:
A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of a solution to a singularly perturbed time-optimal control problem”, Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), 60–69
A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal control problem with a small parameter”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 62–71
A. I. Korotkii, N. A. Artemova, N. A. Vaganova, O. O. Kovrizhnykh, L. I. Rubina, O. N. Ulyanov, O. V. Ushakova, M. Yu. Filimonov, I. A. Tsepelev, “O razrabotkakh analiticheskikh i chislennykh metodov resheniya zadach mekhaniki sploshnoi sredy”, Tr. IMM UrO RAN, 19, no. 2, 2013, 203–215
A. R. Danilin, O. O. Kovrizhnykh, “Asymptotic representation of a solution to a singular perturbation linear time-optimal problem”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 22–35
A. R. Danilin, O. O. Kovrizhnykh, “O zavisimosti zadachi bystrodeistviya dlya lineinoi sistemy ot dvukh malykh parametrov”, Vestnik ChelGU, 2011, no. 14, 46–60
Citation in format AMSBIB
Contact us: