Necessary Optimality Conditions for Singular Controls of Caputo Fractional Systems with Delay in Control

• Autores: Shakir Sh. Yusubov, Elimhan N. Mahmudov
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
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• Resumen

  • In this paper, we consider the optimal control of nonlinear systems of fractionalorder with control delay, where the fractional derivatives are expressed in the Caputo sense. For this problem, we first obtained the necessary first-order optimality condition in the form of the Pontryagin maximum principle. For a control that is singular in the sense of the Pontryagin maximum principle, a higher-order necessary optimality condition is obtained. Further, in one particular case, a multipoint necessary secondorder optimality condition is obtained. The effectiveness of the results obtained is illustrated by specific examples.

• Referencias bibliográficas
  • 1. Aadhithiyan, S., Raja, R., Dianavinnarasi, J., Alzabut, J., Baleanu, D.: Robust synchronization of multi-weighted fractional-order complex...
  • 2. Ahmad, B., Alnahdi, M., Ntouyas, S.K., Alsaedi, A.: On a mixed nonlinear fractional boundary value problem with a new class of closed integral...
  • 3. Ahmed, S., Azar, A.T., Abdel-Aty, M., Khan, H., Alzabut, J.: A nonlinear system of hybrid fractional differential equations with application...
  • 4. Almalahi, M.A., Aldwoah, K.A., Shah, K., Abdeljawad, T.: Stability and numerical analysis of a coupled system of piecewise Atangana-Baleanu...
  • 5. Baleanu, D., Jajarmi, A., Sajjadi, S.S., Mozyrska, D.: A new fractional model and optimal control of a tumor-immune surveillance with non-singular...
  • 6. Baleanu, D., Shekari, P., Torkzadeh, L., Ranjbar, H., Jajarmi, A., Nouri, K.: Stability analysis and system properties of Nipah virus transmission:...
  • 7. Beale, N., Battey, H., Davison, A.C., MacKay, R.S.: An unethical optimization principle. R. Soc. Open Sci. 7(7), 200462 (2020)
  • 8. Bergounioux, M., Bourdin, L.: Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal...
  • 9. Defterli, O., Baleanu, D., Jajarmi, A., Sajjadi, S.S., Alshaikh, N., Asad, J.H.: Fractional treatment: an accelerated mass-spring system....
  • 10. Diethelm, K.: The Analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo...
  • 11. Dhivakaran, P.B., Vinodkumar, A., Vijay, S., Lakshmanan, S., Alzabut, J., El-Nabulsi, R.A., Anukool, W.: Bipartite synchronization of...
  • 12. Flores-Tlacuahuac, A., Biegler, L.T.: Optimization of fractional order dynamic chemical processing systems. Ind. Eng. Chem. Res. 53, 5110–5127...
  • 13. Idczak, D., Walczak, S.: On a linear-quadratic problem with Caputo derivative. Opuscula Math. 36, 49–68 (2016)
  • 14. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.:Theory and applications of fractional differential equations, Volume 204 of North-Holland...
  • 15. Khan, A., Ain, Q.T., Abdeljawad, T., Nisar, K.S.: Exact controllability of hilfer fractional differential system with non-instantaneous...
  • 16. Mahmudov, E.N.: Optimal control of higher order differential inclusions with functional constraints. ESAIM Contr. Optim. Calcul. Var....
  • 17. Mahmudov, E.N.: Approximation and Optimization of Discrete and Differential Inclusions. Elsevier, Boston (2011)
  • 18. Mahmudov, E.N.: Transversality condition and optimization of higher order ordinary differential inclusions. Optimization 64, 2131–2144...
  • 19. Mahmudov, E.N., Yusubov, S.S.: Nonlocal boundary value problems for hyperbolic equations with a Caputo fractional derivative. J. Comput....
  • 20. Mahmudov, E.N., Mastaliyeva, D.: Optimal control of higher-order retarded differential inclusions. J. Ind. Manag. Optim. 19, 6544–6557...
  • 21. Martinez-Legaz, J.E., Chavarriga, J., Garcia, I.A., Gine, J.: Optimizacion matematica y sus aplicaciones economicas. Varia Mathematica...
  • 22. Mishra, K.K., Dubey, S., Baleanu, D.: Existence and controllability of a class of nonautonomous nonlinear evolution fractional integrodifferential...
  • 23. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishenko, E.F.: Mathematical theory of optimal processes, Moscow: Nauka, (1983);...
  • 24. Rakhshan, S., Effati, S.: Fractional optimal control problems with time-varying delay: a new delay fractional Euler-Lagrange equations....
  • 25. Ruixiong, F., Yan, N., Chen, Y., Chengbo, Z.: Qualitative behaviour of a caputo fractional differential system. Qual. Theory Dyn. Syst....
  • 26. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers,...
  • 27. Vivek, D., Kanagarajan, K., Elsayed, E.M.: Attractivity and Ulam-Hyers stability results for fractional delay differential equations....
  • 28. Wang, Q., Xiaoyue, L.: Structure of the solution set to fractional differential inclusions with impulses at variable times on compact...
  • 29. Yakovenko, S. Yu.: Necessary conditions for optimality in the convex Bolza problem with phase constraints of general type, Funktsional....
  • 30. Yusubov, S.S.: Necessary optimality conditions for systems with impulse control. Comput. Math. and Math. Phys. 45, 222–226 (2005)
  • 31. Yusubov, S.S.: Necessary optimality conditions for singular controls. Comput. Math. Math. Phys. 47, 1446–1451 (2007)
  • 32. Yusubov, S.S.: Boundary value problems for hyperbolic equations with a Caputo fractional derivative. Adv. Math. Models Appl. 5, 192–204...
  • 33. Yusubov, S.S., Mahmudov, E.N.: Optimality conditions of singular controls for systems with Caputo fractional derivatives. J. Ind. Manag....
  • 34. Yusubov, S.S., Mahmudov, E.N.: Necessary and sufficient optimality conditions for fractional Fornasini-Marchesini model. J. Ind. Manag....
  • 35. Yusubov, S.S., Mahmudov, E.N.: Some necessary optimality conditions for systems with fractional Caputo derivatives. J. Ind. Manag. Optim....
  • 36. Yusubov, S.S., Mahmudov, E.N.: Necessary optimality conditions for quasi-singular controls for systems with Caputo fractional derivatives....
  • 37. Zhu, B., Han, B.: Approximate controllability for mixed type non-autonomous fractional differential equations. Qual. Theory Dyn. Syst....