UDC 517.9

O.A. Kapustian
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
 olenakapustian@knu.ua,  olena.kap@gmail.com

N.V. Kasimova
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
 kasimova@knu.ua

APPROXIMATE OPTIMAL CONTROL FOR A NONLINEAR HYPERBOLIC INCLUSION
WITH PERTURBED NON-AUTONOMOUS COEFFICIENTS

REFERENCES

• 1. Kapustyan O., Kasimova N., Sobchuk V., Stanzhytskyi O. The averaging method for the optimal control problem of a parabolic inclusion with fast-oscillating coefficients on a finite time interval. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences. 2024. Vol. 79, N 2. P. 33–40. https://doi.org/10.17721/1812-5409.2024/2.6.
• 2. Kapustyan O.A., Kasimova N.V. Approximate optimal control for a nonlinear hyperbolic equation with perturbed non-autonomous coefficients. Scientific Bulletin of Uzhgorod University. Series "Mathematics and Informatics". 2025. Vol. 46, No. 1. P. 305–313. https://doi.org/10.24144/2616-7700.2025.46(1).305-313.
• 3. Ahmed N.U., Kerbal S. Optimal control of nonlinear second order evolution equations. Journal of Applied Mathematics and Stochastic Analysis. 1993. Vol. 6, N 2. P. 123–136. http://dx.doi.org/10.1155/S1048953393000127.
• 4. Papageorgiou N.S. Existence of solutions for second-order evolution inclusions. Journal of Applied Mathematics and Stochastic Analysis. 1994. Vol. 7, N 4. P. 525–535. http://dx.doi.org/10.1155/S1048953394000407.
• 5. Papageorgiou N.S., Yannakakis N. Second order nonlinear evolution inclusions I: Existence and relaxation results. Acta Mathematica Sinica. 2005. Vol. 21, N 5. P. 977–996. https://doi.org/10.1007/s10114-004-0508-y.
• 6. Migorski S. Existence, variational and optimal control problems for nonlinear second order evolution inclusions. Dynam. Syst. and Appl. 1995. Vol. 4. P. 513–528. URL: https://www.dynamicpublishers.com/DSA/Ds41995.htm.
• 7. Kapustian O.A., Nakonechnyi O.G. Approximate minimax estimation of functionals of solutions to the wave equation under nonlinear observations. Cybernetics and Systems Analysis. 2020. Vol. 56, N 5. P. 793–801. https://doi.org/10.1007/s10559-020-00300-2.
• 8. Zadoianchuk N.V., Kasyanov P.O. Dynamics of solutions of a class of second-order autonomous evolution inclusions. Cybernetics and Systems Analysis. 2012. Vol. 48, N 3. P. 414–428. https://doi.org/10.1007/s10559-012-9421-z.
• 9. Zadoyanchuk N.V., Kas’yanov P.O. Faedo–Galerkin method for nonlinear second-order evolution equations with Volterra operators. Nonlinear Oscillations. 2007. Vol. 10, N 2. P. 203–228. https://doi.org/10.1007/s11072-007-0016-y.
• 10. Zadoyanchuk N.V., Kasyanov P.O. On the solvability of differential-operator inclusions of the second order with non-coercive operators of Wo-pseudomonotone type. Reports of the National Academy of Sciences of Ukraine. 2008. No. 4. P. 19–24. URL: https://nasplib.isofts.kiev.ua/items/5f4e9d52-da62-4894-8041-ae65eda4186d.
• 11. Zgurovsky M.Z., Mel’nik V.S. Nonlinear analysis and control of physical processes and fields. Berlin; Heidelberg: Springer, 2004. XIV, 508 p. https://doi.org/10.1007/978-3-642-18770-4.
• 12. Kasimova N., Feketa P. Application of the averaging method to the optimal control of parabolic differential inclusions on the semi-axis. Axioms. 2025. Vol. 14, Iss. 1. Article number 74. https://doi.org/10.3390/axioms14010074.
• 13. Dashkovskiy S., Kapustyan O., Kapustian O., Zhuk T. Asymptotic analysis of optimal control problems on the semiaxes for Caratheodory differential inclusions with fast oscillating coefficients. Nonlinear Analysis: Modelling and Control. 2023. Vol. 28, N 6. P. 1077–1088. https://doi.org/10.15388/namc.2023.28.33435.
• 14. Nakonechnyi A.G., Mashchenko S.O., Chikrij V.K. Motion control under conflict condition.  Journal of Automation and Information Sciences. 2018. Vol. 50, Iss. 1. P. 54–75. https://doi.org/10.1615/JAutomatInfScien.v50.i1.40.
• 15. Kashpur O.F. Solving Hermite interpolation problem in finite-dimensional Euclidean space. Cybernetics and Systems Analysis. 2022. Vol. 58, N 2. P. 259–267. https://doi.org/10.1007/s10559-022-00458-x.
• 16. Aumann R.J. Integrals of set-valued functions. J. Math. Anal. Appl. 1965. Vol. 12, Iss. 1. P. 1–12. https://doi.org/10.1016/0022-247X(65)90049-1.
• 17. Aubin J.-P., Cellina A. Differential inclusions. Set-valued maps and viability theory. Berlin; Heidelberg: Springer, 1984. 355 p. URL: https://link.springer.com/book/10.1007/978-3-642-69512-4.
• 18. Chepyzhov V.V., Vishik M.I. Attractors of equations of mathematical physics. Providence, RI: American Mathematical Society, 2002. 362 p. URL: https://catalog.princeton.edu/catalog/SCSB-8709997.
• 19. Hermes H. Calculus of set valued functions and control. Indiana University Mathematics Journal. 1969. Vol. 18, Iss. 1. P. 47–59. https://doi.org/10.1512/IUMJ.1969.18.18006.
• 20. Warga J. Optimal control of differential and functional equations. New York; London: Academic Press, 2014. 546 p. URL: https://api.pageplace.de/preview/DT0400.9781483259192_A23866022/preview-9781483259192_A23866022.pdf.