Abstract:
The paper is devoted to the problem of constructing external estimates for reachable sets of a nonlinear control system. The estimates are constructed in the form of level sets of smooth functions in the space of states satisfying differential inequalities. In the system under consideration, the linear part is found, for which the corresponding functions are assumed to be known. The method proposed for estimating trajectories of a nonlinear system is based on modifying estimates for the linear part and on applying the comparison principle.
Keywords:
control system, reachable set, comparison principle.
\Bibitem{Gus11}
\by M.~I.~Gusev
\paper On external estimates for reachable sets of nonlinear control systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 1
\pages 60--69
\mathnet{http://mi.mathnet.ru/timm672}
\elib{https://elibrary.ru/item.asp?id=17869783}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 275
\issue , suppl. 1
\pages S57--S67
\crossref{https://doi.org/10.1134/S0081543811090057}
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This publication is cited in the following 9 articles:
I. V. Zykov, “External Estimates of Reachable Sets for Control Systems with Integral Constraints”, J Math Sci, 2025
I. V. Zykov, “O vneshnikh otsenkakh mnozhestv dostizhimosti upravlyaemykh sistem s integralnymi ogranicheniyami”, Materialy Voronezhskoi vesennei matematicheskoi shkoly
«Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 190, VINITI RAN, M., 2021, 107–114
I. V. Zykov, “O vneshnikh otsenkakh mnozhestv dostizhimosti upravlyaemykh sistem s integralnymi ogranicheniyami”, Izv. IMI UdGU, 53 (2019), 61–72
M. S. Nikol'skii, “Estimation of Reachable Sets from Above with Respect to Inclusion for Some Nonlinear Control Systems”, Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S98–S104
M. I. Gusev, I. V. Zykov, APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'19, 2164, APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'19, 2019, 060008
Mikhail Gusev, Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015, 579
G. A. Timofeeva, N. A. Timofeev, “Forecasting credit portfolio components with a Markov chain model”, Autom. Remote Control, 73:4 (2012), 637–651
M. I. Gusev, “Metod dinamicheskogo programmirovaniya v zadache postroeniya mnozhestv dostizhimosti nelineinykh upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 1(39), 42–43
L. I. Rodina, “Invariantnye i statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 2(40), 3–164
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