On one Control Problem of a Variable Structure With Fractional Caputo Derivatives
- Authors: Ahmedova Z.B.1,2
-
Affiliations:
- Baku State University
- Institute of Control System of the National Academy of Sciences of Azerbaijan
- Issue: No 2 (65) (2024)
- Pages: 5-16
- Section: Mathematics
- URL: https://journal-vniispk.ru/1993-0550/article/view/307271
- DOI: https://doi.org/10.17072/1993-0550-2024-2-5-16
- ID: 307271
Cite item
Full Text
Abstract
We consider an optimal control problem with a variable structure, described in different time intervals by various ordinary nonlinear fractional differential equations. Using an analogue of the incremental method, a necessary condition for first-order optimality is proved. In the case of convex control domains, a linearized maximum condition is proved, and in the case of open control domains, an analogue of the Euler equation is obtained.
About the authors
Zhalya B. Ahmedova
Baku State University; Institute of Control System of the National Academy of Sciences of Azerbaijan
Author for correspondence.
Email: jaleahmadova23@gmail.com
Candidate of Sciences (Physical and Mathematical), Associate Professor of the Mathematical Cybernetics Department, the Applied Mathematics and Cybernetics Faculty 23, Z. Khalilov St., Baku, Azerbaijan, 1148
References
- Mansimov, K.B. and Rzaeva, V.G. (2020), "Quasi-osome controls in optimal control problems described by hyperbolic integro-differential equations", Bulletin of Perm University. Mathematics. Mechanics. Computer Science, no. 1(48), pp. 13-20.
- Gabelko, K.N. (1975), "Optimization of multistu-penchat processes", Abstract of the dissertation for the degree of Candidate of Phys.-Mat. Sciences. Irkutsk, 17 p.
- Mastaliev, R.O. (2016), "On the problem of optimal control of a linear system with a variable structure" Vladikavkaz Mathematical Journal, no. 1, pp. 63-70.
- Muslumov, V.B. (2006), "Optimality conditions in one system with distributed parameters", Abstract of dissertation for the degree of Candidate of Phys.-Mat. Sciences, Baku, 2006, 21 p.
- Mansimov, K.B. and Ahmedova, J.B. (2022), "About one task of optimal control with a variable structure", Bulletin of Baku State University, series of physical and mathematical sciences, no. 3, pp. 5-16.
- Postnov, S.S. (2015), "Research of the optimum control tasks of the dynamic systems of the fractional order by the method of moments", Author's abstract of the dissertation for the degree of candidate of physical and mathematical sciences, Moscow, 26 p.
- Bahaa, G.M. (2017), "Fractional optimal control problem for differential system with delay argument", Advances in Difference Equations, no. 1, рp. 32-51.
- Agrawal, O.P. (2004), "A General Formula-tion and Solution Scheme for Fractional Optimal Control Problems", Nonlinear Dynamics, no. 38, рp. 323–337.
- Ali H.M., Pereira F.L. and Gama S.M. (2016), "A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems", Mathematical Methods in the Applied Sciences, no. 39, pp. 3640-3649.
- Mansimov, K.B. and Akhmedova, J.B. (2022) "Analog of Pontryagin's maximum principle in the problem of optimal control of the system of differential equations with fractional Caputo derivative and multipoint quality criterion", Bulletin of Perm University. Mathematics. Mechanics. Computer Science, no. 3(58). pp. 5-10.
- Samko, S.G., Kilbas, A.A. and Marichev O.I. (1993), Fractional integrals and derivatives: Theory and applications, Gordon and Breach Science publishers, Yverdon, Switzerland.
- Akhmedova, J.B. (2021), "Pontryagin's maximum principle for one nonlinear fractional optimal control problem", Mathematical Bulletin of Vyatka State University, no. 1(20), pp. 5-11.
- Lin, S.Y. (2013), "Generalized Gronwall inequalities and their applications to fractional differential equations", Journal of Inequalities and Applications, 549, no. 1.
- Gabasov, R. and Kirillova, F.M. (2011), "Osobye optimal'nye upravleniya" [Special optimal con-trols], Librocom, Moscow, Russia.
- Alekseev, V.M., Tikhomirov, V.M. and Fomin, S.V. (2018), "Optimalnoe upravlenie" [Optimal control]. Fizmatlit, Moscow, Russia.
Supplementary files
