Generalized control with compact support for systems with distributed parameters

• Autorzy: Khurshudyan A. Zh.

Identyfikatory

DOI

10.1515/acsc-2015-0001

• Języki publikacji: EN

Abstrakty

EN

We propose a generalization of the Butkovskiy’s method of control with compact support [1] allowing to derive exact controllability conditions and construct explicit solutions in control problems for systems with distributed parameters. The idea is the introduction of a new state function which is supported in considered bounded time interval and coincides with the original one therein. By means of techniques of the distributions theory the problem is reduced to an interpolation problem for Fourier image of unknown function or to corresponding system of integral equalities. Treating it as infinite dimensional problem of moments, its L¹, L² and L^∞-optimal solutions are constructed explicitly. The technique is explained for semilinear wave equation with distributed and boundary controls. Particular cases are discussed.

Słowa kluczowe

EN

distributed system; controls with compact support; problem of moments; L1; L2 and L∞-optimal controls

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2015
• Tom: Vol. 25, no. 1
• Strony: 5--20
• Opis fizyczny: Bibliogr. 23 poz., wzory

Twórcy

autor

Khurshudyan A. Zh.

• Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian str., 0025, Armenia

Bibliografia

• [1] A. G. Butkovskiy: Methods of Control for Systems with Distributed Parameters. Nauka Publisher, Moscow, 1975, (in Russian).
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• [6] As. Zh. Khurshudyan: Generalized control with compact support of wave equation with variable coefficients. Int. J. of Dynamics and Control, (2015), DOI 10.1007/s40435-015-0148-3.
• [7] As. Zh. Khurshudyan: On optimal boundary control of non–homogeneous string vibrations under impulsive concentrated perturbations with delay in controls. Mathematical Bulletin of T. Shevchenko Scientific Society, 10 (2013), 203-209.
• [8] As. Zh. Khurshudyan and Sh. Kh. Arakeylan: Delaying control of non– homogeneous string forced vibrations under mixed boundary conditions. International Siberian Conference on Control and Communication, Krasnoyarsk, Russia, (2013), 1-5.
• [9] As. Zh. Khurshudyan: On optimal boundary and distributed control of partial integro–differential equations.Archives of Control Sciences, 24(1), (2014), 5-25.
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Uwagi

EN

The application of this method in particular problems were done in collaboration with my friends and colleagues Am. Khurshudyan and Sh. Arakelyan, whom I heartily thankful. To the blessed memory of innocent victims of Armenian Genocide (1915) is dedicated.