zbMATH — the first resource for mathematics

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.

49K40 Sensitivity, stability, well-posedness
49K15 Optimality conditions for problems involving ordinary differential equations
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.