On the construction of an asymptotic solution of a linear singularly perturbed optimal control problem with degeneracy in the quality criterion

Tarasenko Oksana Volodymyrivna

Tarasenko Oksana Volodymyrivna ¹

¹ Department of Higher Mathematics, Nizhyn State University named after Mykola Gogol, Chernihiv region, Nizhin, 16600, Ukraine

Keywords: asymptotic solution, a linear singularly perturbed optimal control problem

Download

Abstract

We obtain some results concerning the investigation of built an asymptotic solution of optimal control problem which is describing by a linear singularly perturbed system of differential equations with degenerate matrix of derivatives, in the case of simple elementary divisors. The case of degenerations of main matrix of criterion quality is suggested. The problem is taken to consideration of boundary-value problems, which turns out after the application of Pontryagin’s maximum principle. For this purpose, it was used results of asymptotic analysis of the general solution for a linear singularly perturbed system of differential equations with degenerations.

References

[1] Tarasenko O. V. On the asymptotic solution of a linear singularly perturbed optimal control problem with degeneracy // Scientific Bulletin of Uzhhorod University. Series: Mathematics and Informatics. - 2013. - 24, N2. - P. 193-205.

[2] Samoilenko A. M., Shkil M. I., Yakovets V. P. Linear systems of differential equations with degeneracies - K.: Higher School, 2000. - 294 p.

[3] Shkil N. I., Starun I. I., Yakovets V. P. Asymptotic integration of linear systems of differential equations with degeneracies. P. Asymptotic integration of linear systems of differential equations with degeneracies. - K.: Vyshcha Shk., 1991. - 207 p.

[4] Pontryagin L. S., Boltyansky V. G. Gamkrelidze R. V. Mishchenko E. F. Mathematical theory of optimal processes. - M.: Nauka, 1983. - 392 p.

[5] Boyarintsev Y. E., Danilov V. A., Loginov A. A., Chistyakov V. F. Numerical methods for solving singular systems. - Novosibirsk: Nauka. Siberian Branch, 1989. - 223 p.

[6] Boyarintsev Y. E., Chistyakov V. F. Algebro-differential systems. Methods of numerical solution and research. - Novosibirsk: Nauka, 1998. - 222 p.

Download

Cite

ACS Style: Tarasenko, O.V. On the construction of an asymptotic solution of a linear singularly perturbed optimal control problem with degeneracy in the quality criterion. Bukovinian Mathematical Journal. 2016, 2
AMA Style: Tarasenko OV. On the construction of an asymptotic solution of a linear singularly perturbed optimal control problem with degeneracy in the quality criterion. Bukovinian Mathematical Journal. 2016; 2(2-3).
Chicago/Turabian Style: Oksana Volodymyrivna Tarasenko. 2016. "On the construction of an asymptotic solution of a linear singularly perturbed optimal control problem with degeneracy in the quality criterion". Bukovinian Mathematical Journal. 2 no. 2-3.

Export

BibTex EndNote RIS