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.
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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).
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 8, pp. 1099–1109, August, 2008.
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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
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DOI: https://doi.org/10.1007/s11253-009-0126-z