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 Izv. IMI UdGU, 2019, Volume 53, Pages 61–72 (Mi iimi371)

On external estimates of reachable sets of control systems with integral constraints

I. V. Zykov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia

Abstract: In this paper, we consider the problem of constructing external estimates of reachable sets as a level set of a certain differentiable Lyapunov–Bellman function (depending only on the state vector) for a control system with an integral control constraint. In particular, with its suitable choice, one can obtain ellipsoidal and rectangular estimates. The proposed constructions are based on integral estimates, the maximum solution, and the comparison principle for systems of differential inequalities. By using time in the arguments of the Lyapunov–Bellman function, it is possible to obtain more accurate estimates. In the linear nonstationary case, the latter can coincide with the set of reachability. A number of illustrative examples for nonlinear systems are given.

Keywords: reachable set, controlled system, integral constraints, integral inequalities, comparison principle, external estimates.

DOI: https://doi.org/10.20537/2226-3594-2019-53-06

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UDC: 517.977.1
MSC: 93C15, 49N30, 34A40

Citation: I. V. Zykov, “On external estimates of reachable sets of control systems with integral constraints”, Izv. IMI UdGU, 53 (2019), 61–72

Citation in format AMSBIB
\Bibitem{Zyk19} \by I.~V.~Zykov \paper On external estimates of reachable sets of control systems with integral constraints \jour Izv. IMI UdGU \yr 2019 \vol 53 \pages 61--72 \mathnet{http://mi.mathnet.ru/iimi371} \crossref{https://doi.org/10.20537/2226-3594-2019-53-06} \elib{http://elibrary.ru/item.asp?id=38503199}