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 The Bulletin of Irkutsk State University. Series Mathematics: Year: Volume: Issue: Page: Find

 The Bulletin of Irkutsk State University. Series Mathematics, 2017, Volume 19, Pages 205–216 (Mi iigum299)

Estimates of reachable sets for systems with impulsive control, uncertainty and nonlinearity

T. F. Filippova

Krasovskii Institute of Mathematics and Mechanics UB RAS, 16, S. Kovalevskaya st., Ekaterinburg, 620990

Abstract: The problem of estimating trajectory tubes for nonlinear controlled dynamical systems with uncertainty in the initial data is studied. It is assumed that the dynamic system has a special structure in which the nonlinear terms are defined by quadratic forms on state coordinates and the values of uncertain initial states and admissible controls are constrained by ellipsoidal restrictions. Matrix of linear terms in the state system velocities is also not exactly known, but it belongs to the known compact in the corresponding space, i.e. the dynamics of the system is complicated by the presence of bilinear components in the right-hand sides of the system of differential equations. We solve the problem of estimating the reachable sets of nonlinear control system of this kind, the results make it possible to construction of the corresponding numerical algorithms. We solve here the problem of estimating the reachable sets of nonlinear controlled system of this kind, the results make it possible to construct the corresponding numerical algorithms.

Keywords: control system, reachable set, impulse control, state estimation, uncertainty.

 Funding Agency Grant Number Russian Science Foundation 16-11-10146

DOI: https://doi.org/10.26516/1997-7670.2017.19.205

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Document Type: Article
UDC: 517.977
MSC: 93B03, 93C41, 49N25

Citation: T. F. Filippova, “Estimates of reachable sets for systems with impulsive control, uncertainty and nonlinearity”, The Bulletin of Irkutsk State University. Series Mathematics, 19 (2017), 205–216

Citation in format AMSBIB
\Bibitem{Fil17} \by T.~F.~Filippova \paper Estimates of reachable sets for systems with impulsive control, uncertainty and nonlinearity \jour The Bulletin of Irkutsk State University. Series Mathematics \yr 2017 \vol 19 \pages 205--216 \mathnet{http://mi.mathnet.ru/iigum299} \crossref{https://doi.org/10.26516/1997-7670.2017.19.205}