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

Author(s)
Alexander Chentsov

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.

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.

Cite this paper

nullA. Chentsov, "Filters and Ultrafilters as Approximate Solutions in the Attainability Problems with Constraints of Asymptotic Character,"*Intelligent Information Management*, Vol. 2 No. 9, 2010, pp. 526-551. doi: 10.4236/iim.2010.29062.

nullA. Chentsov, "Filters and Ultrafilters as Approximate Solutions in the Attainability Problems with Constraints of Asymptotic Character,"

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.

[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.