Step averaging differential inclusions with variable dimension on a finite interval (in Russian) |
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Author |
aaplotnikov@ukr.net
Odessa National University named after I.I.Mechnikov
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Abstract |
Nonlinear differential inclusion with variable dimension and justification of the step scheme
of the averaging method on a finite interval is considered in this paper.
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Keywords |
averaging method; differential inclusion; variable dimension
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DOI |
doi:10.15330/ms.46.1.81-88
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Reference |
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2. Blagodatskikh V.I., Filippov A.F. Differential inclusions and optimal control// Proc. Steklov Inst. Math. – 1986. – V.169. – P. 199–259. 3. Perestyuk N.A., Plotnikov V.A., Samoilenko A.M., Skripnik N.V. Differential equations with impulse effects: multivalued right-hand sides with discontinuities. – de Gruyter Stud. Math.: 40, Berlin/Boston: Walter De Gruyter GmbH& Co., 2011. 4. Plotnikov V.A., Plotnikov A.V., Vityuk A.N., Differential equations with a multivalued right-hand side: Asymptotic methods. – AstroPrint, Odessa. 1999. (in Russian) 5. Smirnov G.V. Introduction to the theory of differential inclusions. – Graduate Studies in Mathematics, Vol. 41, American Mathematical Society. Providence, Rhode Island, 2002. 6. Krylov N.M., Bogoliubov N.N. Introduction to nonlinear mechanics. – Princeton University Press, Princeton, 1947. 7. Arnol’d, V.I. Mathematical methods of classical mechanics. – Nauka, Moscow, 1989. (in Russian) 8. Filatov A.N. Asymptotic methods in the theory of differential and integrodifferential equations. – Izdat. “Fan” Uzbek. SSR. Tashkent, 1974. (in Russian) 9. Filatov A.N., Sharova L.V. Integral inequalities and the theory of nonlinear oscillations. – Nauka, Moscow, 1976. (in Russian) 10. Filatov O.P., Khapaev M.M. Averaging of systems of differential inclusions. – Izdatel’stvo Moskovskogo Universiteta imeni M. V. Lomonosova, Moscow, 1998. (in Russian) 11. Gama R., Smirnov G. Stability and optimality of solutions to differential inclusions via averaging method// Set-Valued Var. Anal. – 2014. – V.22, ¹2. – P. 349–374. 12. Klymchuk S., Plotnikov A., Skripnik N. Overview of V.A. Plotnikov’s research on averaging of differential inclusions// Phys. D. – 2012. – V.241, ¹22. – P. 1932–1947. 13. Lochak P., Meunier C. Multiphase averaging for classical systems. – Appl. Math. Sci., V.72, Springer- Verlag, New York, 1988. 14. Sanders J.A., Verhulst F. Averaging methods in nonlinear dynamical systems. – Appl. Math. Sci., V.59, Springer-Verlag, New York, 1985. 15. Fedoseev A.V. Research methods of optimum control of one model of working out of group of deposits of a mineral with the limited stores// Methods of the system analysis and problems of rational use of resources, Vychislitel’nyj Tsentr AN SSSR, Moskva. – 1977. – P. 117–134. (in Russian) 16. Khachaturov V.R., Bosolejl R., Fedoseev A.V. Simulation modelling and optimum control problems at long-term planning of manufacture of long-term agricultural crops. – Vychislitel’nyj Tsentr AN SSSR, Moskva, 1985. (in Russian) 17. Romanenko A.V., Fedoseev A.V. Optimal control of economic systems with a growth structure// Comput. Math. Math. Phys. – 1993. – V.33, ¹8. – P. 1017–1026. 18. Kichmarenko O.D., Plotnikov A.V. Nonlinear differential inclusion with variable dimension and their properties// Visn. Odes. Nats. Univ. Matematika i Mekhanika. – 2013. – V.18, ¹2. – P. 29—34. (in Russian) 19. Kichmarenko O.D., Plotnikov A.A. The averaging of control linear differential equations with variable dimension on finite interval// International Journal of Sensing, Computing and Control. – 2015. – V.5, ¹1. – P. 25–35. |
Pages |
81-88
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Volume |
46
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Issue |
1
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Year |
2016
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Journal |
Matematychni Studii
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Full text of paper | |
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