We consider the problem of optimal control over differential equations with interaction. It is shown that the optimal control satisfies the maximum principle and there exists a generalized optimal control. In the analyzed problem, we encounter certain new technical features as compared with the ordinary problem of optimal control.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. A. Dorogovtsev, “Stochastic flows with interactions and measure-valued processes,” Int. J. Math. Math. Sci., 63, 3963–3977 (2003).
A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).
V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control [in Russian], Nauka, Moscow (1979).
N. P. Erugin and I. Z. Shtokalo, A Course of Ordinary Differential Equations [in Russian], Vyshcha Shkola, Kiev (1974).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 8, pp. 1099–1109, August, 2008.
Rights and permissions
About this article
Cite this article
Ostapenko, E.V. Problem of optimal control for a determinate equation with interaction. Ukr Math J 60, 1285–1298 (2008). https://doi.org/10.1007/s11253-009-0126-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-009-0126-z