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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Volume 17, Number 1, Pages 60–69 (Mi timm672)  
This article is cited in 9 scientific papers (total in 9 papers)

On external estimates for reachable sets of nonlinear control systems

M. I. Gusev

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (181 kB) Citations (9)
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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.
Received: 24.12.2010
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, Volume 275, Issue 1, Pages S57–S67
DOI: https://doi.org/10.1134/S0081543811090057
Bibliographic databases:
Document Type: Article
UDC: 517.977.1
Language: Russian
Citation: M. I. Gusev, “On external estimates for reachable sets of nonlinear control systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 1, 2011, 60–69; Proc. Steklov Inst. Math. (Suppl.), 275, suppl. 1 (2011), S57–S67
Citation in format AMSBIB
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\pages 60--69
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  • https://www.mathnet.ru/eng/timm/v17/i1/p60
    • This publication is cited in the following 9 articles:
    1. I. V. Zykov, “External Estimates of Reachable Sets for Control Systems with Integral Constraints”, J Math Sci, 2025  crossref
    2. 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  mathnet  crossref
    3. I. V. Zykov, “O vneshnikh otsenkakh mnozhestv dostizhimosti upravlyaemykh sistem s integralnymi ogranicheniyami”, Izv. IMI UdGU, 53 (2019), 61–72  mathnet  crossref  elib
    4. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    5. 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  crossref
    6. Mikhail Gusev, Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015, 579  crossref
    7. G. A. Timofeeva, N. A. Timofeev, “Forecasting credit portfolio components with a Markov chain model”, Autom. Remote Control, 73:4 (2012), 637–651  mathnet  crossref  isi
    8. M. I. Gusev, “Metod dinamicheskogo programmirovaniya v zadache postroeniya mnozhestv dostizhimosti nelineinykh upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 1(39), 42–43  mathnet
    9. L. I. Rodina, “Invariantnye i statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 2(40), 3–164  mathnet
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