Abstract:
Algorithms for constructing the optimal result function are proposed for a planar time-optimal problem with a circular velocity vectogram and a nonconvex target set with smooth boundary. The algorithms work with the case where the solution of the problem has a complicated (segmented) structure of the singular set. Differentiable dependences are detected for smooth segments of the singular set, which makes it possible to consider and construct these segments as arcs of integral curves. An example of the time-optimal problem is considered, for which the optimal result function and its singular set are calculated numerically. A visualization of the results is implemented.
Citation:
P. D. Lebedev, A. A. Uspenskii, “Construction of the optimal result function and dispersing lines in time-optimal problems with a nonconvex target set”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 2, 2016, 188–198
\Bibitem{LebUsp16}
\by P.~D.~Lebedev, A.~A.~Uspenskii
\paper Construction of the optimal result function and dispersing lines in time-optimal problems with a nonconvex target set
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 2
\pages 188--198
\mathnet{http://mi.mathnet.ru/timm1304}
\crossref{https://doi.org/10.21538/0134-4889-2016-22-2-188-198}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3559175}
\elib{https://elibrary.ru/item.asp?id=26040833}
Linking options:
https://www.mathnet.ru/eng/timm1304
https://www.mathnet.ru/eng/timm/v22/i2/p188
This publication is cited in the following 5 articles:
Pavel D. Lebedev, Alexander A. Uspenskii, Lecture Notes in Control and Information Sciences - Proceedings, Stability and Control Processes, 2022, 427
P. D. Lebedev, A. A. Uspenskii, “Postroenie rasseivayuschikh krivykh v odnom klasse zadach bystrodeistviya pri skachkakh krivizny granitsy tselevogo mnozhestva”, Izv. IMI UdGU, 55 (2020), 93–112
P. D. Lebedev, V. N. Ushakov, A. A. Uspenskii, “Numerical methods for constructing suboptimal packings of nonconvex domains with curved boundary”, J. Appl. Industr. Math., 14:4 (2020), 681–692
P. D. Lebedev, A. A. Uspenskii, “Postroenie resheniya zadachi upravleniya po bystrodeistviyu pri narushenii gladkosti krivizny granitsy tselevogo mnozhestva”, Izv. IMI UdGU, 53 (2019), 98–114
P. D. Lebedev, A. A. Uspenskii, “Algoritmy resheniya zadachi
bystrodeistviya s krugovoi vektogrammoi skorostei v neodnorodnoi srede”, Chelyab. fiz.-matem. zhurn., 4:4 (2019), 387–397
Citation in format AMSBIB
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