{"title":"Rayleigh–Ritz Operator in Inverse Problems for Higher Order Multilinear Nonautonomous Evolution Equations","authors":"A. V. Lakeyev, Yu. E. Linke, V. A. Rusanov","doi":"10.1134/s1055134423040053","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study solvability questions for the problem on realization of operator functions for\nan invariant polylinear regulator of a higher-order differential system in an infinite-dimensional\nseparable Hilbert space. This is a nonstationary coefficient-operator inverse problem for\nmultilinear evolution equations whose dynamic order is higher than one (notice that\nnonautomonous hyperbolic systems belong to this class of problems). We analyze semiadditivity\nand continuity for a nonlinear Rayleigh–Ritz functional operator and obtain an analytic model of\nan invariant polylinear regulator. This model allows us to combine two bundles of trajectory\ncurves induced by different invariant polylinear regulators in a differential system and obtain\na family of admissible solutions of the initial differential system in terms of an invariant polylinear\naction. The obtained results can be applied in the general qualitative theory of nonlinear\ninfinite-dimensional adaptive control systems described by higher-order multilinear\nnonautonomous differential systems (including neuromodelling).\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134423040053","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study solvability questions for the problem on realization of operator functions for
an invariant polylinear regulator of a higher-order differential system in an infinite-dimensional
separable Hilbert space. This is a nonstationary coefficient-operator inverse problem for
multilinear evolution equations whose dynamic order is higher than one (notice that
nonautomonous hyperbolic systems belong to this class of problems). We analyze semiadditivity
and continuity for a nonlinear Rayleigh–Ritz functional operator and obtain an analytic model of
an invariant polylinear regulator. This model allows us to combine two bundles of trajectory
curves induced by different invariant polylinear regulators in a differential system and obtain
a family of admissible solutions of the initial differential system in terms of an invariant polylinear
action. The obtained results can be applied in the general qualitative theory of nonlinear
infinite-dimensional adaptive control systems described by higher-order multilinear
nonautonomous differential systems (including neuromodelling).
期刊介绍：
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.
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