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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 3, Pages 344–354 (Mi vuu593)  

MATHEMATICS

On the solvability of the problem of guaranteed package guidance to a system of target sets

V. I. Maksimov, P. G. Surkov

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

Abstract: Control theory is a section of modern mathematics being actively developed at present time. The class of problems investigated within the framework of this theory is quite extensive and includes issues related to the existence of solutions as well as issues related to the effective methods for constructing controls. One of the approaches to solving control problems under lack of information was suggested by Yu. S. Osipov in the fundamental paper published in the Russian Mathematical Surveys in 2006. Later, this approach, called the method of program packages, was developed, in particular, in the articles cited in this paper. This approach is based on a suitable modification of the method of non-anticipatory strategies (quasi-strategies) for solving control problems with unknown initial states. As is known, quasi-strategies reflecting the Volterra properties of program realizations of closed-loop controls in corresponding program disturbances are oriented to the investigation of problems with known initial states under the presence of unknown dynamical disturbances. Such disturbances are usually absent in standard control problems with incomplete information and incompleteness of information is due to a lack of information about the initial state of the system. So, program packages became an analogue of the properties of nonanticipativeness for problems with unknown initial states. It should be noted that in all previous works related to the method of program packages, the guidance problems to one single target set were considered. In the present paper the guaranteed guidance problem to a collection of target sets under incomplete information about the initial state is considered for a linear autonomous control dynamical system. The criterion for the solvability of that problem is established. It is based on the method of program packages. An illustrative example is given.

Keywords: linear systems, control, incomplete information.

Funding Agency Grant Number
Russian Science Foundation 14-11-00539


DOI: https://doi.org/10.20537/vm170305

Full text: PDF file (282 kB)
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Document Type: Article
UDC: 517.977
MSC: 91A24, 93C41, 49N75
Received: 01.08.2017

Citation: V. I. Maksimov, P. G. Surkov, “On the solvability of the problem of guaranteed package guidance to a system of target sets”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017), 344–354

Citation in format AMSBIB
\Bibitem{MakSur17}
\by V.~I.~Maksimov, P.~G.~Surkov
\paper On the solvability of the problem of guaranteed package guidance to a system of target sets
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 3
\pages 344--354
\mathnet{http://mi.mathnet.ru/vuu593}
\crossref{https://doi.org/10.20537/vm170305}
\elib{http://elibrary.ru/item.asp?id=30267245}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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