Second-order maximum principle controlled weakly singular Volterra integral equations

• Autorzy: Gasimov Jasarat J. , Mahmudov Nazim I.

Identyfikatory

DOI

10.24425/acs.2024.153105

• Języki publikacji: EN

Abstrakty

EN

This work studies a class of singular Volterra integral equations that are (controlled) and can be applied to memory-related problems. For optimum controls, we prove a second-order Pontryagin type maximal principle.

Słowa kluczowe

EN

second-order maximum principle; singular Volterra integral equation; optimal control; Pontryagin’s maximum principle

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2024
• Tom: Vol. 34, No. 4
• Strony: 863--880
• Opis fizyczny: Bibliogr. 8 poz., wzory

Twórcy

autor

Gasimov Jasarat J.

• Department of Mathematics, Eastern Mediterranean University, Mersin 10, 99628, T.R. North Cyprus, Turkey

• https://orcid.org/0009-0008-1084-2005

autor

Mahmudov Nazim I.

• Department of Mathematics, Eastern Mediterranean University, Mersin 10, 99628, T.R. North Cyprus, Turkey

• https://orcid.org/0000-0003-3943-1732

Bibliografia

• [1] P. Lin and J. Yong: Controlled singular Volterra integral equations and Pontryagin maximum principle. SIAM Journal on Control and Optimization, 58(1), (2020), 136-164. DOI: 10.1137/19M124602X
• [2] J.J.Gasimov, J.A. Asadzade and N.I. Mahmudov: Pontryagin maximum principle for fractional delay differential equations and controlled weakly singular Volterra delay integral equations. arXiv preprint, (2023). DOI: 10.48550/arXiv.2309.14007
• [3] M.J. Mardanov, K.B. Mansimov and N.H. Abdullayeva: Integral necessary condition of optimality of the second order for control problems described by system of integro-differential equations with delay. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 22(2), (2018), 254-268. DOI: 10.14498/vsgtu1597
• [4] A.A. Abdullayev and K.B. Mansimov: Multipoint necessary optimality conditions for singular controls in processes described by the system of volterra integral equations. Cybernetics and Systems Analysis, 49(6), (2013), 845-851.
• [5] M.J. Mardanov and T.K. Melikov: On the theory of singular optimal controls in dynamic systems with control delay. Computational Mathematics and Mathematical Physics. 57(5), (2017), 749-69. DOI: 10.1134/S0965542517050086
• [6] J. Moon: A Pontryagin maximum principle for terminal state-constrained optimal control problems of Volterra integral equations with singular kernels. AIMS Mathematics, 8(10), (2023), 22924-22943. DOI: 10.3934/math.20231166
• [7] S.S. Susubov and E.N. Mahmudov: Necessary optimality conditions for quasi-singular controls for systems with Caputo fractional derivatives. Archives of Control Sciences, 33(3), (2023), 463-496. DOI: 10.24425/acs.2023.146955
• [8] S.S. Yusubov and E.N. Mahmudov: Optimality conditions of singular controls for systems with Caputo fractional derivatives. Journal of Industrial and Management Optimization, 19(1), (2023). DOI: 10.3934/jimo.2021182