ON FEEDBACK CONTROL SYSTEMS GOVERNED BY FRACTIONAL DIFFERENTIAL INCLUSIONS

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

For feedback systems governed by fractional semilinear differential inclusions and a sweeping process in a Hilbert space, controllability conditions are found. For the proof, topological methods of nonlinear analysis for multivalued condensing maps are used.

Авторлар туралы

G. Petrosyan

Voronezh State Pedagogical University

Email: garikpetrosyan@yandex.ru

Әдебиет тізімі

  1. Balachandran, K. Controllability of nonlinear systems in Banach spaces: a survey / K. Balachandran, J.P. Dauer //J. Optim. Theory Appl. — 2002. — V. 115. — P. 7-28.
  2. Benedetti, I. Controllability for impulsive semilinear functional differential inclusions with a noncompact evolution operator / I. Benedetti, V. Obukhovskii, P. Zecca // Discuss. Math. Differ. Incl. Control Optim. — 2011. — V. 31. — P. 39-69.
  3. Gorniewicz, L. Controllability of semilinear differential equations and inclusions via semigroup theory in Banach spaces / L. Gorniewicz, S.K. Ntouyas, D. O’Regan // Rep. Math. Phys. — 2005. — V. 56. — P. 437-470.
  4. Monteiro Marques, M.D.P. Differential inclusions in nonsmooth mechanical problems. Shocks and dry friction / M.D.P. Monteiro Marques // Progress Nonlin. Differ. Equat. Appl. — 1993. — V. 9.
  5. Valadier, M. Rafle et viabilite / M. Valadier // Sem. Anal. Convexe Exp. — 1992. — V. 22, № 17.
  6. Edmond, J.F. Relaxation of an optimal control problem involving a perturbed sweeping process / J.F. Edmond, L. Thibault // Math. Program. Ser. B. — 2005. — V. 104. — P. 347-373.
  7. Tolstonogov, A.A., Local existence conditions for sweeping process solutions, Sb. Math., 2019, vol. 210, no. 9, pp. 1305–1325.
  8. Kilbas, A.A. Theory and Applications of Fractional Differential Equations / A.A. Kilbas, H.M. Sriva-stava, J.J. Trujillo. — Amsterdam : Elsevier Science B.V., North-Holland Mathematics Studies, 2006.
  9. Podlubny, I. Fractional Differential Equations / I. Podlubny. — San Diego : Academic Press, 1999.
  10. Gomoyunov, M.I. Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems / M.I. Gomoyunov // Fract. Calc. Appl. Anal. — 2018. — V. 21. — P. 1238-1261.
  11. On semilinear fractional differential inclusions with a nonconvex-valued right-hand side in Banach spaces / V. Obukhovskii, G. Petrosyan, C.F. Wen, V. Bocharov // J. Nonlin. Var. Anal. — 2022. — V. 6, № 3. — P. 185-197.
  12. Petrosyan, G., On a boundary value problem for a class of fractional Langevin type differential equations in a Banach space, Vestn. Udmurt. Un-ta. Matematika. Mekhanika. Komp’yuternye Nauki, 2022, vol. 32, no. 3, pp. 415–432.
  13. Zhou, Y. Existence of mild solutions for fractional neutral evolution equations / Y. Zhou, F. Jiao // Comput. Math. Appl. — 2010. — V. 59. — P. 1063-1077.
  14. Kamenskii, M. Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces / M. Kamenskii, V. Obukhovskii, P. Zecca. — Berlin ; New-York : Walter de Gruyter, 2001.
  15. Borisovich, Yu.G., Gel’man, B.D., Myshkis, A.D., and Obukhovskii, V.V., Vvedeniye v teoriyu mnogoznachnykh otobrazheniy i differentsial’nykh vklyucheniy (Introduction to the Theory of Multivalued Maps and Differential Inclusions), Moscow: Librocom, 2011.
  16. Mainardi, F. On the initial value problem for the fractional diffusion-wave equation / F. Mainardi, S. Rionero, T. Ruggeri // Waves and Stability in Continuous Media. — 1994. — P. 246-251.
  17. Nigmatullin, R.R. The realization of the generalized transfer equation in a medium with fractal geometry / R.R. Nigmatullin // Phys. Status Solidi B. — 1986. — V. 133. — P. 425-430.

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML

© Russian Academy of Sciences, 2024