Averaging of control systems of multivalued trajectories

A.V.Arsirij; A.V.Plotnikov

In the present paper given article we consider the optimal control problem with a terminal criterion of quality in which the condition of system is described by valued map and admissible controls are summable functions. Here we prove theorems of the complete averaging method for the problems of such type.

1. Плотников В.А., Плотников А.В., Витюк А.Н. Дифференциальные уравнения с многозначной правой частью. Асимптотические методы. - Одесса: ''АстроПринт'', 1999. - 354 с.

2. Толстоногов А.А. Дифференциальные включения в Банаховом пространстве. - Новосибирск: Наука, 1986. - 296 с.

3. Brandao Lopes Pinto A.J., de Blasi F.S., Iervolino F. Uniqueness and existence theorems for differential equations with compact convex valued solutions // Boll. U.M.I. - 1970. - № 4. - P.534-538.

4. de Blasi F.S., Iervolino F. Equazioni differentiali con soluzioni a valore compatto convesso // Boll.Unione Mat.Ital. - 1969. - V.2, № 4-5. - P.491-501.

5. Hukuhara M. Integration des applications mesurables dont la valeur est un compact convexe // Func. Ekvacioj. - 1967. - № 10. - P.205-223.

6. Kaleva O. Fuzzy differential equations // Fuzzy Sets and Systems. - 1987. - V.24, № 3. - P.301-317.

7. Kaleva O. The Cauchy problem for fuzzy differential equations // Fuzzy Sets and Systems. - 1990. - V.35. - P.389-396.

8. Kisielewicz M. Description of a class of differential equations with set-valued solutions // Lincei-Rend. Sc. fis. mat. e nat. - 1975. - V. LVIII. - P.158-162.

9. Kisielewicz M. Method of averaging for differential equations with compact convex valued solutions // Rend. Math. - 1976. - V.9, № 3. - P.397-408.

	Averaging of control systems of multivalued trajectories (in Russian)
Author	A.V.Arsirij, A.V.Plotnikov Odessa I.I.Mechnykov National University
Abstract	In the present paper given article we consider the optimal control problem with a terminal criterion of quality in which the condition of system is described by valued map and admissible controls are summable functions. Here we prove theorems of the complete averaging method for the problems of such type.
Keywords	optimal control problem, terminal criterion of quality, admissible control, valued map
DOI	doi:10.30970/ms.33.1.65-70
Reference	1. Плотников В.А., Плотников А.В., Витюк А.Н. Дифференциальные уравнения с многозначной правой частью. Асимптотические методы. - Одесса: ''АстроПринт'', 1999. - 354 с. 2. Толстоногов А.А. Дифференциальные включения в Банаховом пространстве. - Новосибирск: Наука, 1986. - 296 с. 3. Brandao Lopes Pinto A.J., de Blasi F.S., Iervolino F. Uniqueness and existence theorems for differential equations with compact convex valued solutions // Boll. U.M.I. - 1970. - № 4. - P.534-538. 4. de Blasi F.S., Iervolino F. Equazioni differentiali con soluzioni a valore compatto convesso // Boll.Unione Mat.Ital. - 1969. - V.2, № 4-5. - P.491-501. 5. Hukuhara M. Integration des applications mesurables dont la valeur est un compact convexe // Func. Ekvacioj. - 1967. - № 10. - P.205-223. 6. Kaleva O. Fuzzy differential equations // Fuzzy Sets and Systems. - 1987. - V.24, № 3. - P.301-317. 7. Kaleva O. The Cauchy problem for fuzzy differential equations // Fuzzy Sets and Systems. - 1990. - V.35. - P.389-396. 8. Kisielewicz M. Description of a class of differential equations with set-valued solutions // Lincei-Rend. Sc. fis. mat. e nat. - 1975. - V. LVIII. - P.158-162. 9. Kisielewicz M. Method of averaging for differential equations with compact convex valued solutions // Rend. Math. - 1976. - V.9, № 3. - P.397-408.
Pages	65-70
Volume	33
Issue	1
Year	2010
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Averaging of control systems of multivalued trajectories (in Russian)