# Issue 3 (197), article 2

Cybernetics and Computer Engineering, 2019, 3 (197), pp.

Barseghyan V.R., DSc (Phys and Math), Professor,
Leading Researcher of the Institute of Mechanics
of the National Academy of Sciences of Armenia,
Professor of the Faculty of Mathematics
and Mechanics of Yerevan State University
email: barseghyan@sci.am
Yerevan State University, Institute of Mechanics of NAS of Armenia
18, Bakunts st., 0033, Yerevan, Republic of Armenia

THE PROBLEM OF CONTROL OF MEMBRANE VIBRATIONS WITH NON-SEPARATED MULTIPOINT CONDITIONS AT INTERMEDIATE MOMENTS OF TIME

Introduction. Many control processes from various fields of science and technology lead to the necessity to study multipoint boundary value problems of control, in which, along with classical boundary conditions, non-separated multi-point intermediate conditions are also given. A characteristic feature of multipoint boundary value problems of control is the presence of non-separated conditions at several intermediate points of the study interval. Such control problems have important applied and theoretical value, a necessity naturally arises for their investigation in various settings. In this article, the problem of control of vibrations of a rectangular membrane with given initial, final conditions and non-separated values of the deflection function and velocities at intermediate moments of time is considered.

The purpose of the article is to develop a constructive approach to construct a function of control action to control the vibrations of a rectangular membrane with given initial, final conditions and non-separated (non-local) values of the deflection and velocities of membrane points at intermediate moments of time.

Results. By the method of separation of variables, the problem is reduced to the problem of control of ordinary differential equations with given initial, final, and non-separated multipoint intermediate conditions. Using the methods of the theory of control of finite-dimensional systems with multipoint intermediate conditions, a control action to control vibrations of a rectangular membrane is constructed.

Keywords: control of vibrations, membrane vibration, intermediate values, non-separated multipoint conditions.

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