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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Lakeyev A. V.
,
Linke Y. E.
,
Rusanov V. A.
ON REALIZATION OF MULTIPLE-LINEAR REGULATOR OF NON-STATIONARY HYPERBOLIC SYSTEM // BSU bulletin. Mathematics, Informatics. - 2019. №3. . - С. 3-16.
Title:
ON REALIZATION OF MULTIPLE-LINEAR REGULATOR OF NON-STATIONARY HYPERBOLIC SYSTEM
Financing:
Работа выполнена при финансовой поддержке РФФИ (проекты: 19-01-00301, 19-08-00746).
Codes:
DOI: 10.18101/2304-5728-2019-3-3-16UDK: 517.93, 517.937
Annotation:
The article studies some qualitative issues of the existing a solution to inverse prob- lem of nonlinear infinite-dimensional system analysis, regarding the solvability of the operator realization of invariant multiple-linear regulator of non-stationary hy- perbolic system. The studied statement for precision mathematical modeling con- siders the case, when for two different beams (finite, countable, or even continuous) of nonlinear controlled dynamic processes of the “trajectory, program control” type, induced in a real separable Hilbert space by some given non-stationary hyperbolic system, but with different multiple-linear regulators, we obtain sufficient conditions for solvability of the problem of realizing operator functions of a general (invariant) multiple-linear regulator, in which presence in equation structure of a given hyper- bolic system the union of these dynamic beams represent a fixed family of its ad- missible solutions. The study was carried out in the light of modern ideas about the geometry of infinite-dimensional vector fields and based on a qualitative study of the semi-additivity of non-linear Rayleigh-Ritz functional operator.
Keywords:
qualitative theory of nonlinear differential realization; non-stationary hyperbolic system; Rayleigh-Ritz functional operator; multiple-linear regulator.
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