Abstract:
The problem of estimating trajectory tubes of a nonlinear control system with uncertainty in initial data is considered. It is assumed that the dynamical system has a special structure, in which nonlinear terms are quadratic in phase coordinates and the values of the uncertain initial states and admissible controls are subject to ellipsoidal constraints. Differential equations are found that describe the dynamics of the ellipsoidal estimates of reachable sets of the nonlinear dynamical system under consideration. To estimate reachable sets of the nonlinear differential inclusion corresponding to the control system, we use results from the theory of ellipsoidal estimation and the theory of evolution equations for multivalued states of dynamical systems under uncertainty.
Citation:
T. F. Filippova, “Differential equations of ellipsoidal estimates for reachable sets of a nonlinear dynamical control system”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 223–232; Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S75–S84
\Bibitem{Fil10}
\by T.~F.~Filippova
\paper Differential equations of ellipsoidal estimates for reachable sets of a~nonlinear dynamical control system
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 1
\pages 223--232
\mathnet{http://mi.mathnet.ru/timm539}
\elib{https://elibrary.ru/item.asp?id=13073001}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 271
\issue , suppl. 1
\pages S75--S84
\crossref{https://doi.org/10.1134/S0081543810070072}
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Linking options:
https://www.mathnet.ru/eng/timm539
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This publication is cited in the following 26 articles:
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V. N. Ushakov, A. A. Ershov, A. V. Ushakov, “On Integral Funnels of Controlled Systems Changed within Several Small Time Intervals”, Mech. Solids, 58:8 (2023), 2826
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V. N. Ushakov, A. V. Ushakov, O. A. Kuvshinov, “O konstruirovanii razreshayuschego upravleniya v zadache o sblizhenii v fiksirovannyi moment vremeni”, Izv. IMI UdGU, 58 (2021), 73–93
Tatiana F. Filippova, Springer Proceedings in Complexity, 13th Chaotic Modeling and Simulation International Conference, 2021, 195
Tatiana F. Filippova, 2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB), 2020, 1
Gornov A.Yu., Finkelstein E.A., Zarodnyuk T.S., “Algorithm of Uniform Filling of Nonlinear Dynamic System Reachable Set Based on Maximin Problem Solution”, Optim. Lett., 13:3, SI (2019), 633–643
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Filippova T.F., “The Hjb Approach and State Estimation For Control Systems With Uncertainty”, IFAC PAPERSONLINE, 51:13 (2018), 7–12
Filippova T.F., “Differential Equations For Ellipsoidal Estimates of Reachable Sets For a Class of Control Systems With Nonlinearity and Uncertainty”, IFAC PAPERSONLINE, 51:32 (2018), 770–775
Filippova T.F., “Ellipsoidal Estimates of Reachable Sets For Control Systems With Nonlinear Terms”, IFAC PAPERSONLINE, 50:1 (2017), 15355–15360
Alexandr Yu. Gornov, Tatiana S. Zarodnyuk, Evgeniya A. Finkelstein, Anton S. Anikin, “The method of uniform monotonous approximation of the reachable set border for a controllable system”, J Glob Optim, 66:1 (2016), 53
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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
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V. N. Ushakov, A. R. Matviychuk, G. V. Parshikov, “A method for constructing a resolving control in an approach problem based on attraction to the solvability set”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 135–144
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P. D. Lebedev, A. V. Ushakov, “Approximating sets on a plane with optimal sets of circles”, Autom. Remote Control, 73:3 (2012), 485–493
V. N. Ushakov, P. D. Lebedev, A. R. Matviychuk, A. G. Malev, “Differential games with fixed terminal time and estimation of the instability degree of sets in these games”, Proc. Steklov Inst. Math., 277 (2012), 266–277
Matviychuk O.G., “Estimation Problem for Impulsive Control Systems Under Ellipsoidal State Bounds and with Cone Constraint on the Control”, Applications of Mathematics in Engineering and Economics (AMEE'12), AIP Conference Proceedings, 1497, eds. Pasheva V., Venkov G., Amer Inst Physics, 2012, 3–12
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