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Title: Asymptotics of the Solution to a Singularly Perturbed Time-Optimal Control Problem with Two Small Parameters
Authors: Danilin, A. R.
Kovrizhnykh, O. O.
Issue Date: 2020
Publisher: Pleiades Publishing
Citation: Danilin A. R. Asymptotics of the Solution to a Singularly Perturbed Time-Optimal Control Problem with Two Small Parameters / A. R. Danilin, O. O. Kovrizhnykh. — DOI 10.1134/S0081543820040033 // Proceedings of the Steklov Institute of Mathematics. — 2020. — Vol. 309. — P. S10-S23.
Abstract: The paper continues the authors’ previous studies. We consider a time-optimal control problem for a singularly perturbed linear autonomous system with two independent small parameters and smooth geometric constraints on the control in the form of a ball cases formulae-sequence superscript R2 superscript R2 missing-subexpressionmissing-subexpressionsuperscript 3 formulae-sequencenorm 1formulae-sequence0 much-less-than 1missing-subexpressionmissing-subexpressionformulae-sequence 0subscript 0 superscriptsubscript 01superscript 3 0subscript 0missing-subexpressionmissing-subexpressionmissing-subexpressionformulae-sequence subscript 0formulae-sequence subscript 0 subscript missing-subexpressionmissing-subexpressionmissing-subexpression where 0100 The main difference of this case from the systems with fast and slow variables studied earlier is that here the matrix at the fast variables is the second-order Jordan block with zero eigenvalue and, thus, does not satisfy the standard asymptotic stability condition. Continuing the research, we consider initial conditions depending on the second small parameter. We derive and justify a complete asymptotic expansion in the sense of Erdelyi of the optimal time and optimal control with respect to the asymptotic sequence superscript superscript superscript, 01. © 2020, Pleiades Publishing, Ltd.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85089812517
PURE ID: 13658216
ISSN: 815438
DOI: 10.1134/S0081543820040033
metadata.dc.description.sponsorship: This work was partially supported by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and Ural Federal University).
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