
Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 2, Pages 210–221
(Mi vuu581)




MATHEMATICS
On approximate solvability set construction in a guidance problem for a timeinvariant control system on a finite time interval
G. V. Parshikov^{} ^{} N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia
Abstract:
A timeinvariant control system on a finite time interval in the finitedimensional Euclidean space is considered. We discuss a problem of guidance with a compact target set for a control system on a given time interval. One way to solve the considered guidance problem is based on finding a solvability set in the phase space, namely, a set of all system positions from which, as from the initial ones, the guidance problem is solvable. The construction of the solvability set is an independent timeconsuming problem which rarely has an exact solution. In this paper we discuss the approximate construction of a solvability set in the guidance problem for a timeinvariant nonlinear control system. It is wellknown that this problem is closely connected with the problem of constructing integral funnels and trajectory tubes of control systems. Integral funnels of control systems can be approximately constructed stepbystep as sets of corresponding attainability sets, therefore, attainability sets are considered to be the basic elements of the solving construction in this paper.
Here, we propose a scheme of the solvability set approximate construction in a guidance problem for a timeinvariant control system on a finite time interval. The basis of this scheme is reduction to the solvability sets approximate calculation of a finite number of simpler problems, namely, problems of guidance with the target set at fixed time moments from the given time interval. Wherein, the moments of time have to be chosen quite tightly in the mentioned time interval. As an example, we provide mathematical modeling of the guidance problem of the control system named “Translational Oscillator with Rotating Actuator” as well as the graphical support of the problem solution.
Keywords:
control system, guidance problem, attainability set, solvability set, solvability set approximation.
DOI:
https://doi.org/10.20537/vm170205
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UDC:
517.977.58
MSC: 37M05, 49M25, 93C15 Received: 16.05.2017
Citation:
G. V. Parshikov, “On approximate solvability set construction in a guidance problem for a timeinvariant control system on a finite time interval”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:2 (2017), 210–221
Citation in format AMSBIB
\Bibitem{Par17}
\by G.~V.~Parshikov
\paper On approximate solvability set construction in a guidance problem for a timeinvariant control system on a finite time interval
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 2
\pages 210221
\mathnet{http://mi.mathnet.ru/vuu581}
\crossref{https://doi.org/10.20537/vm170205}
\elib{http://elibrary.ru/item.asp?id=29410192}
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