A. Kerimbekov, E.F. Abdylaeva. On solvability of the tracking problem in nonlinear vector optimization of oscillation processes ... P. 103-115

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

Received February 9, 2024

Revised March 25, 2024

Accepted April 15, 2024

Akylbek Kerimbekov, Dr. Phys.-Math. Sci., Prof., Department of Applied Mathematics and Informatics, Kyrgyz-Russian Slavic University, Bishkek, Kyrgyzstan, e-mail: akl7@rambler.ru

Elmira Faizuldaevna Abdyldaeva, Сand. Sci. (Phys.-Math.), Department of Mathematics, Kyrgyz-Turkish Manas University, Bishkek, Kyrgyzstan, e-mail: elmiraabdyldaeva@manas.edu.kg, efa_69@mail.ru

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Cite this article as: A. Kerimbekov, E.F. Abdylaeva. On solvability of the tracking problem in nonlinear vector optimization of oscillation processes. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 2, pp. 103–115.