T. F. Filippova, “Construction of set-valued estimates of reachable sets for some nonlinear dynamical systems with impulsive control”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 262–269; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S95

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 4, Pages 262–269 (Mi timm442)

This article is cited in 23 scientific papers (total in 23 papers)

Construction of set-valued estimates of reachable sets for some nonlinear dynamical systems with impulsive control

T. F. Filippova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Full-text PDF (188 kB) Citations (23)

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Abstract: A method of constructing ellipsoidal estimates of reachable sets is proposed for a nonlinear system with a scalar impulsive control and uncertainty in initial data. A special discontinuous change of time is used to transform the impulsive system under consideration into an ordinary differential inclusion without impulsive components. To estimate reachable sets of the obtained nonlinear differential inclusion, results from the theory of ellipsoidal estimation and theory of evolution equations of set-valued states of dynamical systems under uncertainty are used.

Keywords: reachable set, impulsive control, trajectory tubes, set-valued estimates, differential inclusions.

Received: 20.05.2009

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, Volume 269, Issue 1, Pages S95–S102
DOI: https://doi.org/10.1134/S008154381006009X

Bibliographic databases:

Document Type: Article

UDC: 517.977

Language: Russian

Citation: T. F. Filippova, “Construction of set-valued estimates of reachable sets for some nonlinear dynamical systems with impulsive control”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 262–269; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S95–S102

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/timm442

https://www.mathnet.ru/eng/timm/v15/i4/p262

This publication is cited in the following 23 articles:

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
V. N. Ushakov, A. A. Ershov, A. V. Ushakov, “Control Systems Depending on a Parameter: Reachable Sets and Integral Funnels”, Mech. Solids, 57:7 (2022), 1672
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
V. N. Ushakov, A. A. Ershov, “Reachable sets and integral funnels of differential inclusions depending on a parameter”, Dokl. Math., 104:1 (2021), 200–204
Tatiana F. Filippova, Studies in Computational Intelligence, 838, Recent Advances in Computational Optimization, 2020, 121
Tatiana F. Filippova, Lecture Notes in Computer Science, 11189, Numerical Methods and Applications, 2019, 97
V. A. Dykhta, O. N. Samsonyuk, “Pozitsionnyi printsip minimuma dlya impulsnykh protsessov”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 25 (2018), 46–62
Ushakov V.N., Ukhobotov V.I., Matviychuk A.R., Parshikov G.V., “On Some Nonlinear Control System Problems on a Finite Time Interval”, IFAC PAPERSONLINE, 51:32 (2018), 832–837
Ushakov V.N., Ukhobotov V.I., Ushakov A.V., Parhsikov G.V., “On Game Approach Problems on a Finite Time Interval”, AIP Conference Proceedings, 2040, eds. Simos T., Kalogiratou Z., Monovasilis T., Amer Inst Physics, 2018, 050003
Oxana G. Matviychuk, 2018 14th International Conference “Stability and Oscillations of Nonlinear Control Systems” (Pyatnitskiy's Conference) (STAB), 2018, 1
Tatiana F. Filippova, Lecture Notes in Computer Science, 10665, Large-Scale Scientific Computing, 2018, 210
O. N. Samsonyuk, M. V. Staritsyn, “Impulsnye upravlyaemye sistemy s traektoriyami ogranichennoi $p$ -variatsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 164–177
T. F. Filippova, “Otsenki mnozhestv dostizhimosti sistem s impulsnym upravleniem, neopredelennostyu i nelineinostyu”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 205–216
G. V. Parshikov, “O priblizhennom vychislenii mnozhestva razreshimosti v zadache o sblizhenii statsionarnoi upravlyaemoi sistemy na konechnom promezhutke vremeni”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 210–221
Matviychuk A.R., Ukhobotov V.I., Ushakov A.V., Ushakov V.N., “The Approach Problem of a Nonlinear Controlled System in a Finite Time Interval”, Pmm-J. Appl. Math. Mech., 81:2 (2017), 114–128
V. N. Ushakov, A. R. Matviichuk, “K resheniyu zadach upravleniya nelineinymi sistemami na konechnom promezhutke vremeni”, Izv. IMI UdGU, 2015, no. 2(46), 202–215
T. F. Filippova, “Estimates of reachable sets of control systems with nonlinearity and parametric perturbations”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 67–75
A. V. Ushakov, “Ob odnom variante priblizhennogo postroeniya razreshayuschikh upravlenii v zadache o sblizhenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 4, 94–107
Tatiana F. Filippova, Oksana G. Matviychuk, Lecture Notes in Computer Science, 7116, Large-Scale Scientific Computing, 2012, 123
N. I. Zhelonkina, A. N. Sesekin, S. P. Sorokin, “Ob ustoichivosti lineinykh sistem s impulsnym vozdeistviem v matritse sistemy i zapazdyvaniem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 1, 40–46

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