Abstract:
The nonlinear dynamical control system with uncertainty in initial states and parameters is studied. It is assumed that the dynamic system has a special structure in which the system nonlinearity is due to the presence of quadratic forms in system velocities. The case of combined controls is studied here when both classical measurable control functions and the controls generated by vector measures are allowed. We present several theoretical schemes and the estimating algorithms allowing to find the upper bounds for reachable sets of the studied control system. The research develops the techniques of the ellipsoidal calculus and of the theory of evolution equations for set-valued states of dynamical systems having in their description the uncertainty of set-membership kind. Numerical results of system modeling based on the proposed methods are included.
Keywords:
Control systems, Nonlinearity of quadratic type, Uncertainty, Impulse control, Ellipsoidal calculus, Tube of trajectories.
Bibliographic databases:
Document Type:
Article
Language: English
Citation:
Tatiana F. Filippova, “Control and estimation for a class of impulsive dynamical systems”, Ural Math. J., 5:2 (2019), 21–30
\Bibitem{Fil19}
\by Tatiana F. Filippova
\paper Control and estimation for a class of impulsive dynamical systems
\jour Ural Math. J.
\yr 2019
\vol 5
\issue 2
\pages 21--30
\mathnet{http://mi.mathnet.ru/umj100}
\crossref{https://doi.org/10.15826/umj.2019.2.003}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4054648}
\zmath{https://zbmath.org/?q=an:1451.93175}
\elib{https://elibrary.ru/item.asp?id=41672791}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85078743107}
Linking options:
https://www.mathnet.ru/eng/umj100
https://www.mathnet.ru/eng/umj/v5/i2/p21
This publication is cited in the following 6 articles:
Tatyana Komleva, Irina Molchanyuk, Andrej Plotnikov, Natalia Skripnik, “Guaranteed controls for the control problem of a linear set-valued system”, Filomat, 37:22 (2023), 7685
N. Huseyin, A. Huseyin, Kh. G. Guseinov, “On the properties of the set of trajectories of nonlinear control systems with integral constraints on the control functions”, Tr. IMM UrO RAN, 28, no. 3, 2022, 274–284
Tatiana F. Filippova, “HJB-inequalities in estimating reachable sets of a control system under uncertainty”, Ural Math. J., 8:1 (2022), 34–42
Elena K. Kostousova, “On solving an enhanced evasion problem for linear discrete-time systems”, Ural Math. J., 8:1 (2022), 55–63
B. I. Ananyev, P. A. Yurovskikh, “About an estimation problem of a linear system with delay of information”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 42 (2022), 3–16
E. K. Kostousova, “O poliedralnom metode sinteza upravlenii v zadache tselevogo ukloneniya v lineinykh mnogoshagovykh sistemakh”, Tr. IMM UrO RAN, 27, no. 3, 2021, 101–114
Citation in format AMSBIB
Contact us: