Abstract:
A control system can be treated as a mapping that maps a control to a trajectory (output) of the system. From this point of view, the reachable set, which consists of the ends of all trajectories at a given time, can be considered an image of the set of admissible controls into the state space under a nonlinear mapping. The paper discusses some properties of such abstract reachable sets. The principal attention is paid to the description of the set boundary.
Keywords:
Reachable set, nonlinear mapping, control system, extremal problem, maximum principle.
Bibliographic databases:
Document Type:
Article
Language: English
Citation:
Mikhail I. Gusev, “Computing the reachable set bounda for an abstract control system: revisited”, Ural Math. J., 9:2 (2023), 99–108
\Bibitem{Gus23}
\by Mikhail~I.~Gusev
\paper Computing the reachable set bounda for an abstract control system: revisited
\jour Ural Math. J.
\yr 2023
\vol 9
\issue 2
\pages 99--108
\mathnet{http://mi.mathnet.ru/umj207}
\crossref{https://doi.org/10.15826/umj.2023.2.008}
\elib{https://elibrary.ru/item.asp?id=59690656}
\edn{https://elibrary.ru/MWLCHT}
Linking options:
https://www.mathnet.ru/eng/umj207
https://www.mathnet.ru/eng/umj/v9/i2/p99
This publication is cited in the following 2 articles:
M. I. Gusev, “O nekotorykh svoistvakh mnozhestv dostizhimosti nelineinykh sistem s ogranicheniyami na upravlenie v $L_p$”, Tr. IMM UrO RAN, 30, no. 3, 2024, 99–112
M. I. Gusev, “On Some Properties of Reachable Sets for Nonlinear Systems with Control Constraints in $L_{p}$”, Proc. Steklov Inst. Math., 327:S1 (2024), S124
Citation in format AMSBIB
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