AN OPTIMIZATION APPROACH TO CONSTRUCTING LYAPUNOV–KRASOVSKY FUNCTIONALS

  • D. Ya. Khusainov Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • A. V. Shatyrko Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • Tetiana Shakotko Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
  • Rahima Mustafaeva Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
Keywords: equations of neutral type, Lyapunov–Krasovsky functional, asymptotic stability, non-smooth optimization, optimal functionals

Abstract

A scalar linear differential equation of the neutral type is considered. When studying the stability and obtaining estimates of the convergence of the solutions of the equation, the functional of the Lyapunov–Krasovsky form is used in the quadratic form plus the integral term. The stability conditions of the zero solution are given. Finding the parameters of the functional is reduced to an optimization problem.

References

Vasiliev F. P. Numerical methods for solving extreme problems. Moscow: Nauka. Main edition of physical and mathematical literature, 1988. 552 P.

Bellman R. Dynamic programming. Moscow: IL, 1960. 400 P.

Gabasov R., Kirillova F. M., Kostyukova O. I., Raketsky V. M. Constructive methods of optimization, Vol. 4, Convex Problems. University Press, 1987. 223 P.

Moiseev N. N., Ivanov Yu. P., Stolyarova E. M. Optimization methods. Moscow: Nauka. Main edition of physical and mathematical literature, 1978. 352 P.

Pshenichny B. N., Danilin Yu. M. Numerical methods in extremal problems. Moscow: Nauka, 1975. 319 P.

Hale J. K. Theory of Functional Differential Equations. Moscow: Mir, 1984. 421 P.

Khusainov D. Ya., Shatyrko A. V. Stability of nonlinear control systems with post-exposure. Kyiv: State enterprise “Information and analytic agency", 2012. 73 P.

Shatyrko A. V., Khusainov D. Ya. Optimization methods for studying the absolute stability of regulatory systems. Bulletin of Taras Shevchenko National University of Kyiv. No. 1(13). 2013. P.51-63.

Shor N. Z., Stetsenko S. I. Quadratic extremal problems and non-differentiable optimization. Kyiv: Naukova dumka, 1989. 208 P.

Kratz W. Quadratic Functionals in Variational Analysis and Control Theory. Berlin: Akademie Verlag GmbH, 1995. 293 P.

Published
2023-01-30
How to Cite
Khusainov, D., Shatyrko, A., Shakotko, T., & Mustafaeva, R. (2023). AN OPTIMIZATION APPROACH TO CONSTRUCTING LYAPUNOV–KRASOVSKY FUNCTIONALS. Journal of Numerical and Applied Mathematics, 1(2), 165-173. https://doi.org/10.17721/2706-9699.2022.2.19