On the Problem of Optimal Stabilization of a System of
Linear Loaded Differential Equations
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.
Vanya Barseghyan, Dr. Sci. (Phys.–Math.), Prof., Leading Scientific Researcher, Institute of Mechanics of NAS of RA, 24 B, Marshal Baghramyan ave., Yerevan, 0019, Armenia; Professor of Mathematics and Mechanics Department, Erevan State University, 1, Alec Manukyan st., Yerevan, 0025, Armenia, e-mail: firstname.lastname@example.org
Tamara Simonyan, Cand. Sci. (Phys.–Math.), Assoc. Prof., Mathematics and Mechanics Department, Erevan State University, 1, Alec Manukyan st., Yerevan, 0025, Armenia, e-mail: email@example.com
Tigran Barseghyan, Cand. Sci. (Phys.–Math.), Scientific Researcher of Institute of Mechanics of NAS of RA, 24 B, Marshal Baghramyan ave., Yerevan, 0019, Armenia, e-mail: firstname.lastname@example.org
Barseghyan V.R., Simonyan T.A., Barseghyan T.V. On the Problem of Optimal Stabilization of a System of Linear Loaded Differential Equations. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 27, pp. 71-79. (in Russian) https://doi.org/10.26516/1997-7670.2019.27.71
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