OALib Journal期刊
ISSN: 2333-9721
费用：99美元

投递稿件

查看量	下载量

相关文章
Filters and Ultrafilters as Approximate Solutions in the Attainability Problems with Constrains of Asymptotic Character
Constraints of Asymptotic Character and Attainability Problems
Filters and Ultrafilters in Real Analysis
Ramseyan ultrafilters
The spectrum of characters of ultrafilters on omega
On union ultrafilters
Generating ultrafilters in a reasonable way
Two types of approximate identities depending on the character spaces of Banach algebras
Approximate linear minimum variance filters for continuous-discrete state space models: convergence and practical algorithms
Ultrafilters on omega
更多...

Intelligent Information Management 2010

Filters and Ultrafilters as Approximate Solutions in the Attainability Problems with Constraints of Asymptotic Character

DOI: 10.4236/iim.2010.29062, PP. 526-551

Alexander Chentsov

Keywords: Control problems, Ultrafilters, Topology

Full-Text Cite this paper Add to My Lib

Abstract:

Abstract problems about attainability in topological spaces are considered. Some nonsequential version of the Warga approximate solutions is investigated: we use filters and ultrafilters of measurable spaces. Attrac- tion sets are constructed. AMS (MOS) subject classification. 46A, 49 K 40.

References

[1]	J. Warga, “Optimal Control of Differential and Functional Eguations,” Academic Press, New York, 1972.
[2]	R. V. Gamkrelidze, “Foundations of Optimal Control Theory,” Izdat. Tbil. Univ., Tbilissi, Russian, 1977.
[3]	N. N. Krasovskii, “The Theory of the Control of Motion,” Nauka, Moscow, Russian, 1968.
[4]	R. J. Duffin, “Linear Inequalites and Related Systems,” Annals of Mathematics Studies, Vol. 38, 1956, pp. 157- 170.
[5]	E. G. Gol‘stein, “Duality Theory in Mathematical Programming and Its Applications,” Nauka, Moscow, Russian, 1971.
[6]	N. N. Krasovskii and A. I. Subbotin, “Game-Theoretical Control Problems,” Springer Verlag, Berlin, 1988.
[7]	A. G. Chentsov, “Constructing Operations of the Limit Passage with the Emploument of Ultrafilters of Measurable Spaces,” Avtomatika i telemekhanika, Vol. 6, No. 11, 2007, pp. 208-222.
[8]	A. G. Chentsov and S. I. Tarasova, “Extensions of Abstract Analog of Unstable Control Problems,” Functional Differential Equations, Vol. 16, No. 2, 2009, pp. 237-261.
[9]	A. G. Chentsov, “Asymptotic Attainability,” Kluwer, Dor- drecht, 1997.
[10]	K. Kuratowski and A. Mostowski, “Set Theory,” North- Holland, Amsterdam, 1967.
[11]	N. Bourbaki, “General Topology,” Nauka, Moskow, Russian, 1968.
[12]	J. L. Kelley, “General Topology,” Van Nostrand, Prnceton, NJ, 1957.
[13]	R. Engelking, “General Topology,” PWN, Warszawa, 1977.
[14]	G. Cr?tzer, “General Lattice Theory,” Akademie-Verlag, Berlin, 1978.
[15]	J. Neveu, “Bases Math Matiques Du Calcul Des Probabilit s,” Masson, Paris, 1964.
[16]	A. G. Chentsov and S. I. Morina, “Extensions and Rela- xations,” Kluwer Academic Publishers, Dordrecht/ Boston/London, 2002.
[17]	A. G. Chentsov, “Some Constructions of Asymptotic An- alisis Connected with Stone-?ech Compactification,” Co- ntemporary Mathematics and its Applications, Vol. 26, 2004, pp. 119-150.
[18]	A. G. Chentsov, “Extensions of Abstract Problems of Attainability: Nonsequential Version. Proceedings of the Steklov Institute of Mathematics,” Suppl. 2, 2007, pp. S46-S82. Pleiades Publishing, Ltd., 2007.

Full-Text