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In this paper the property of controllability an ensemble of trajectories of differential inclusion with control parameter is researched. The control problem of an ensemble trajectories from the initial state 0x to a given terminal set )(tYY are studied. The necessary and sufficient conditions for “point” ),(0Yx-controllability and completely Y-controllability are given.
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- Gabasov R., Kirillova F. M. Qualitative theory of optimal processes. Moskow, Nauka (1971).
- Kurzhanskiy A.B. Control and observation under conditions of indeterminacy, Nauka, Moskow (1977).
- Clarke F. Optimization and nonsmooth analysis, Willey & Sons, Ney York (1983).
- Keyn V.N. Optimization of the control system by minimax criterion, Nauka, Moskow (1985).
- Blagodatskikh V.I, Filippov A.F. Differential inclusions and optimal control, Trudy Mat. Inst, AN SSSR, vol.169 (1985). pp. 194-252.
- Papageorgiou N.S. On the trajectories of controlled evolution inclusions, Comment. Math., Univ. Santi-Pauli. vol. 39, №1(1990). pp. 53-67.
- Duda E.V., Minchenko L.I. On optimal trajectories of differential inclusions with delay. Differential equations. Vol. 33, No. 8 (1997).pp. 1023-1029.
- Plotnikov A.B. The controlled kvazidifferential equations and its some property, Differens. Uravneniya, vol. № 10 (1998). pp. 1332-1336.
- Otakulov S. About the conditions of controllability for differential inclusions, Izv. RAN, ser. Texn. Kibernetika, № 2 (1992). pp. 57–62.
- Otakulov S., Sobirova G.D. About some properties of the set M-controllability for differential inclusions, Uzb. Math. Juorn., №1( 2001). pp. 35–41.
- Aseev S. M., An optimal control problem for a differential inclusion with a phase constraint. Smooth approximations and necessary optimality conditions, J. Math. Sci. (New York), vol. 103, № 6 (2001). pp. 670–685 .
- Borosovich Yu.G, Gelman B.D, Mishkis A.D.,Obukhovskiy V.V. Introduction in theory multivalued maps and differential inclusions, KомКniga, Moskow. 2005.
- Plotnikov A.V., Komleva T.A. Piecewise constant controlled linear fuzzy differential inclusions. Universal Journal of Applied Mathematics. vol.1, №2 (2013). pp. 39-43.
- Israilov I, Kholiyarova F.Kh. Minimax control problem for differential inclusion with delayed argument. Materials of the international conference “Dynamic Systems: Stability, Control, Optimization” (DSSCO-2013). Minsk, October 1-5, 2013. pp. 139-141.
- Poloninkin E.S. Set-valued analysis and differential inclusions, Fizmatlit, Moskow (2014).
- Polovinkin E. S. Differential inclusions with unbounded right-hand side and necessary optimality conditions, Proc. Steklov Inst. Math., vol. 291 (2015), pp. 237-252.
- Otakulov S. The control problem by ensemble of trajectories for differential inclusions, Lambert Academic Publishing, Riga (2019).
- Otakulov S., Rahimov B. Sh. About conditions of controllability of ensamble trajectories of differential inclusion. Asian Journal of Multidimensional Research. Vol. 9, Issue 4(April 2020), Spl Issue 4. Pp. 205–213.