Abstract:
A nonlinear control system depending on a parameter is considered in a finite-dimensional Euclidean space and on a finite time interval. The dependence on the parameter of the reachable sets and integral funnels of the corresponding differential inclusion system is studied. Under certain conditions on the control system, the degree of this dependence on the parameter is estimated. Problems of targeting integral funnels to a target set in the presence of an obstacle in strict and soft settings are considered. An algorithm for the numerical solution of this problem in the soft setting has been developed. An estimate of the error of the developed algorithm is obtained. An example of solving a specific problem for a control system in a two-dimensional phase space is given.
Keywords:
control system, differential inclusion, reachable set, integral funnel, parameter dependence, approximation.
This research was supported by the Russian Science Foundation (project no. 19-11-00105).
Bibliographic databases:
Document Type:
Article
Language: English
Citation:
Vladimir N. Ushakov, Aleksandr A. Ershov, Andrey V. Ushakov, Oleg A. Kuvshinov, “Control system depending on a parameter”, Ural Math. J., 7:1 (2021), 120–159
\Bibitem{UshErsUsh21}
\by Vladimir~N.~Ushakov, Aleksandr~A.~Ershov, Andrey~V.~Ushakov, Oleg~A.~Kuvshinov
\paper Control system depending on a parameter
\jour Ural Math. J.
\yr 2021
\vol 7
\issue 1
\pages 120--159
\mathnet{http://mi.mathnet.ru/umj143}
\crossref{https://doi.org/10.15826/umj.2021.1.011}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4301219}
\zmath{https://zbmath.org/?q=an:1471.93135}
\elib{https://elibrary.ru/item.asp?id=46381220}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85112664276}
Linking options:
https://www.mathnet.ru/eng/umj143
https://www.mathnet.ru/eng/umj/v7/i1/p120
This publication is cited in the following 6 articles:
B. T. Samatov, U. B. Soyibboev, “Differential game with “lifeline” for Pontryagin's control example”, Izv. IMI UdGU, 61 (2023), 94–113
B. T. Samatov, Horilov Mahmud Abdumalikovich, Juraev Bahodirjon Inomjon ugli, “Π-strategy for a differential game of pursuit with integral constraints of a generalized type”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:2 (2023), 293–311
B. T. Samatov, A. Kh. Akbarov, B. I. Zhuraev, “Pursuit–evasion differential games with Gr-constraints on controls”, Izv. IMI UdGU, 59 (2022), 67–84
V. N. Ushakov, A. A. Ershov, “O parametricheskoi zavisimosti ob'ema integralnykh voronok i ikh approksimatsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:3 (2022), 447–462
Vladimir Ushakov, Aleksandr Ershov, Andrey Ushakov, Oleg Kuvshinov, 2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), 2022, 1
Bahrom T. Samatov, Ulmasjon B. Soyibboev, “Differential game with a lifeline for the inertial movements of players”, Ural Math. J., 7:2 (2021), 94–109
Citation in format AMSBIB
Contact us: