{"title":"Equivalent Differential Equations in Problems of Control Theory and the Theory of Hamiltonian Systems","authors":"M. G. Yumagulov, L. S. Ibragimova","doi":"10.1134/s0012266124010038","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> New approaches are proposed in the problem of constructing equivalent scalar differential\nequations for multidimensional nonlinear systems of control theory, as well as in the problem of\nconstructing equivalent Hamiltonian systems for nonlinear Lurie equations (scalar differential\nequations containing derivatives of only even orders). The conditions for the solvability of the\ncorresponding problems are studied, and new formulas for the transition to equivalent equations\nand systems are proposed. For the Lurie equations, the proposed approaches are based on the\ntransition from the linear part to the normal forms of the corresponding Hamiltonian systems with\na subsequent transformation of the resulting system. Calculation formulas and algorithms are\nobtained, and their efficiency is illustrated by examples.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124010038","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
New approaches are proposed in the problem of constructing equivalent scalar differential
equations for multidimensional nonlinear systems of control theory, as well as in the problem of
constructing equivalent Hamiltonian systems for nonlinear Lurie equations (scalar differential
equations containing derivatives of only even orders). The conditions for the solvability of the
corresponding problems are studied, and new formulas for the transition to equivalent equations
and systems are proposed. For the Lurie equations, the proposed approaches are based on the
transition from the linear part to the normal forms of the corresponding Hamiltonian systems with
a subsequent transformation of the resulting system. Calculation formulas and algorithms are
obtained, and their efficiency is illustrated by examples.
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