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Averaging method in some problems of optimal control. (English. Ukrainian original) Zbl 1277.49034
Nonlinear Oscil., N.Y. 11, No. 4, 539-547 (2008); translation from Nelinijni Kolyvannya 11, No. 4, 512-519 (2008).
Summary: We substantiate the application of the averaging method to the optimal-control problem for systems of differential equations in the standard Bogolyubov form. An $$\varepsilon$$-optimal control is constructed.

##### MSC:
 49K40 Sensitivity, stability, well-posedness 49K15 Optimality conditions for problems involving ordinary differential equations
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##### References:
 [1] V. A. Plotnikov, Averaging Method in Control Problems [in Russian], Lybid’, Kiev (1992). · Zbl 0808.90121 [2] V. A. Plotnikov, A. V. Plotnikov, and A. N. Vityuk, Differential Equations with Multivalued Right-Hand Sides. Asymptotic Methods [in Russian], AstroPrint, Odessa (1999). [3] V. A. Plotnikov and I. A. Boitsova, ”Averaging by systems with fast and slow variables in optimal-control problems,” Probl. Upravl. Inform., No. 5, 152–156 (2000). [4] M. M. Khapaev, Averaging in Stability Theory [in Russian], Nauka, Moscow (1996). [5] V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control [in Russian], Nauka, Moscow (1979). · Zbl 0516.49002
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