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The Bulletin of Irkutsk State University. Series Mathematics, 2019, Volume 27, Pages 71–79 (Mi iigum367)  

Short Papers

On the problem of optimal stabilization of a system of linear loaded differential equations

V. R. Barseghyanab, T. A. Simonyana, T. V. Barseghyanb

a Yerevan State University, Yerevan, Armenia
b Institute of Mechanics of NAS of RA, Yerevan, Armenia

Abstract: The possibilities of modern computing and measuring technologies allow using the most adequate mathematical models for the actual content of controlled dynamic processes. In particular, the mathematical description of many processes of control from various fields of science and technology can be realized with the help of loaded differential equations. In this paper we study the problem of optimal stabilization of one system of linear loaded differential equations. It is assumed that at the loading points the phase-state function of the system has left-side limits. Similar problems arise, for example, when in case of necessity to conduct an observation of a dynamic process, phase states at some moments of time are measured and information continuously is transmitted through a feedback. These problems have important practical and theoretical significance; hence the necessity for their investigations in various settings naturally arises. Taking into account the nature of the influence of the loaded terms on the dynamics of the process, the system of loaded differential equations is represented in the form of stage-by-stage change differential equations. To solve the problem of optimal stabilization of the motion of a stage-by-stage changing system, the problem is divided into two parts, one of which is formulated on a finite time interval, and the second one - on an infinite interval. The problems set up are solved on the basis of the Lyapunov function method. A constructive approach to construct an optimal stabilizing control is proposed.

Keywords: loaded differential equations, differential equations with memory, optimal stabilization problem, Lyapunov function.

DOI: https://doi.org/10.26516/1997-7670.2019.27.71

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Document Type: Article
UDC: 517.934; 517.977
MSC: 93D05
Received: 13.06.2018

Citation: V. R. Barseghyan, T. A. Simonyan, T. V. Barseghyan, “On the problem of optimal stabilization of a system of linear loaded differential equations”, The Bulletin of Irkutsk State University. Series Mathematics, 27 (2019), 71–79

Citation in format AMSBIB
\Bibitem{BarSimBar19}
\by V.~R.~Barseghyan, T.~A.~Simonyan, T.~V.~Barseghyan
\paper On the problem of optimal stabilization of a system of linear loaded differential equations
\jour The Bulletin of Irkutsk State University. Series Mathematics
\yr 2019
\vol 27
\pages 71--79
\mathnet{http://mi.mathnet.ru/iigum367}
\crossref{https://doi.org/10.26516/1997-7670.2019.27.71}


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