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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ACKNOWLEDGMENTS
The authors express their gratitude to Prof. E.M. Mukhamadiev and Prof. A.B. Nazimov for useful discussion of the issues discussed in the paper.
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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
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Translated by V. Potapchouck
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Yumagulov, M.G., Ibragimova, L.S. Equivalent Differential Equations in Problems of Control Theory and the Theory of Hamiltonian Systems. Diff Equat 60, 23–40 (2024). https://doi.org/10.1134/S0012266124010038
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DOI: https://doi.org/10.1134/S0012266124010038