Abstract:
A time-optimal control problem for a singularly perturbed linear autonomous system is considered. The main difference of this case from systems with fast and slow variables studied earlier is that the eigenvalues of the matrix at the fast variables do not satisfy the standard requirement of the negativity of the real part. We obtain and justify a complete power asymptotic expansion in the sense of Erdelyi of the optimal time and optimal control with respect to the small parameter at derivatives in the equations of the system.
Keywords:
optimal control, time-optimal control problem, asymptotic expansion, singularly perturbed problems, small parameter.
Citation:
A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal control problem with a small parameter”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 61–70; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 62–71
\Bibitem{DanKov16}
\by A.~R.~Danilin, O.~O.~Kovrizhnykh
\paper Asymptotics of the optimal time in a time-optimal control problem with a small parameter
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 1
\pages 61--70
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2017
\vol 297
\issue , suppl. 1
\pages 62--71
\crossref{https://doi.org/10.1134/S0081543817050078}
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Linking options:
https://www.mathnet.ru/eng/timm1260
https://www.mathnet.ru/eng/timm/v22/i1/p61
This publication is cited in the following 1 articles:
D. A. Tursunov, G. A. Omaralieva, K. G. Kozhobekov, “Asymptotics of the Solution of Bisingular Boundary Value Problems with a Biboundary Layer”, Lobachevskii J Math, 43:11 (2022), 3198
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