Abstract:
The tracking problem is investigated in the nonlinear vector optimization of oscillation processes described by integro-differential partial differential equations when the scalar function of external and boundary influence depends nonlinearly on several controls. It is established that this problem has some specific features; in particular, the components of the distributed and boundary vector controls satisfy a system of equal relations and are defined as a solution to a system of two nonlinear integral equations. A method for solving this system is developed. Sufficient conditions are found for the unique solvability of the tracking problem, and an algorithm is developed for constructing a complete solution to the nonlinear optimization problem.
Keywords:
tracking problem, nonlinear optimization, maximum principle, properties of equal ratios, distributed vector optimal control, boundary vector optimal control, optimal process, minimum value of the functional.
Citation:
A. K. Kerimbekov, E. F. Abdyldaeva, “On solvability of the tracking problem in nonlinear vector optimization of oscillation processes”, Trudy Inst. Mat. i Mekh. UrO RAN, 30, no. 2, 2024, 103–115
\Bibitem{KerAbd24}
\by A.~K.~Kerimbekov, E.~F.~Abdyldaeva
\paper On solvability of the tracking problem in nonlinear vector optimization of oscillation processes
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2024
\vol 30
\issue 2
\pages 103--115
\mathnet{http://mi.mathnet.ru/timm2086}
\crossref{https://doi.org/10.21538/0134-4889-2024-30-2-103-115}
\elib{https://elibrary.ru/item.asp?id=67234331}
\edn{https://elibrary.ru/amkosm}
Citation in format AMSBIB
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