For systems of differential equations with pulse action at nonfixed times, we establish the conditions for the existence of optimal control. These conditions depend on the right-hand sides of the system and the quality criterion.
Similar content being viewed by others
References
L. T. Ashchepkov, Optimal Control over Discontinuous Systems [in Russian], Nauka, Novosibirsk (1987).
A. Bensoussan and J. L. Lions, Contrôle Impulsionnel et Inéquations Quasivariationnelles, Dunod, Paris (1982).
N. U. Ahmed, “Optimal control for a general class of impulsive systems on Banach spaces,” in: Proc. of the 42nd IEEE Conf. on Decision and Control (Maui, Hawaii, USA, December 2003), pp. 480–485.
V. A. Dykhta and O. N. Samsonyuk, Optimal Impulsive Control with Applications [in Russian], Fizmatlit, Moscow (2000).
A. A. Aslanyan, “Necessary conditions of optimality in the problems of control over systems of differential equations with pulse action at nonfixed times,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 9, 58–61 1982).
A. A. Aslanyan, “Maximum principle for discontinuous dynamical systems,” Teor. Funkts. Funkts. Anal. Prilozhen., Issue 37, 132–137 (1982).
A. A. Aslanyan, “Conditions of optimality in the problems of control over systems with pulse action,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 11, 3–6 (1982).
Ya. V. Sharifov, “Optimal control for systems with pulse action and nonlocal boundary conditions,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 2, 75–84 (2013).
H. S. Zima, “Existence of the optimal control for some classes of differential equations with pulse action,” Visn. Odes. Nats. Univ., Ser. Mat. Mekh., 18, Issue 2, 20–28 (2013).
K. Yosida, Functional Analysis, Springer, Berlin (1965).
A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).
Author information
Authors and Affiliations
Additional information
Translated from Neliniini Kolyvannya, Vol. 19, No. 4, pp. 493–508, October–December, 2016.
Rights and permissions
About this article
Cite this article
Ivashkevych, A.O., Koval’chuk, T.V. Existence of an Optimal Control for Systems of Differential Equations with Pulse Action at Nonfixed Times. J Math Sci 228, 245–262 (2018). https://doi.org/10.1007/s10958-017-3618-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3618-7