Necessary optimality conditions for a Lagrange problem governed by a continuous Roesser model with Caputo derivatives

• Autorzy: Kamocki Rafał

Identyfikatory

DOI

10.24425/acs.2024.149670

• Języki publikacji: EN

Abstrakty

EN

In the paper, we consider a Lagrange problem governed by a continuous Roesser type system with single partial Caputo derivatives. The necessary optimality conditions for such a problem are derived. In our approach, the increment method, as well as a fractional version of Gronwall’s type lemma for functions of two variables are used.

Słowa kluczowe

EN

partial fractional integrals; derivatives integrals; Roesser type system; maximum principle; Lagrange type cost functional

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2024
• Tom: Vol. 34, No. 3
• Strony: 513--535
• Opis fizyczny: Bibliogr. 15 poz., wzory

Twórcy

autor

Kamocki Rafał

• Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

• https://orcid.org/0000-0002-7800-412X

Bibliografia

• [1] M.A. Ghezzar, A. Berilha, K. Benyettou and D. Bouagada: On the positivity of 2D fractional linear Roesser model using tthe conformable derivative. UPB Scientific Bulletin, Series A 85(2), (2023), 103-114.
• [2] D. Idczak: Necessary optimality conditions for a nonlinear continuous 𝑛-dimensional Roesser model. Mathematics and Computers in Simulation, 41(1-2), (1996), 87-94.
• [3] D. Idczak: A Gronwall lemma for functions of two variables and its application to partial differential equations of fractional order. Mathematical Control and Related Fields, 12(1), (2022), 225-243. DOI: 10.3934/mcrf.2021019
• [4] D. Idczak, R. Kamocki, M. Majewski and S. Walczak: Existence of optimal solutions to Lagrange problems for Roesser type systems of the first and fractional orders. Applied Mathematics and Compuattion, 266 (2015), 809-819. DOI: 10.1016/j.amc.2015.05.142
• [5] D. Idczak, R. Kamocki and M. Majewski: Nonlinear continuous Fornasini-Marchesini model of fractional order with nonzero initial conditions. Journal of Integral Equations Applications, 32(1), (2020), 19-34. DOI: 10.1216/JIE.2020.32.19
• [6] A.D. Ioffe and B.M. Tichomirow: Theory of Extremal Problems. North-Holland Pub. Co: Amsterdam, New York, Oxford, 1979.
• [7] T. Kaczorek and K. Rogowski: Positivity and stabilization of fractional 2D linear systems described by the Roesser model. International Journal of Applied Mathematics and Computer Science, 20(1), (2010), 85-92. DOI: 10.2478/v10006-010-0006-6
• [8] R. Kamocki: Necessary and sufficient optimality conditions for fractional nonhomogeneous Roesser model. Optimal Control Applications and Methods, 37(4), (2016), 574-589. DOI: 10.1002/oca.2180
• [9] R. Kamocki and C. Obczyński: On the single partial Caputo derivatives for functions of two variables. Periodica Mathematica Hungarica, 87 (2023), 324-339. DOI: 10.1007/s10998-023-00520-x
• [10] E. Markin: On antagonistic games for a class of dynamic systems, describing relations in chemical reactors. Vestnic Moskovskogo Universiteta, Seriya, Comput. Math. Cybern., 1 (1978), 44-52. (in Russian).
• [11] E. Markin and A.S. Strekalovki: On the existence, uniqueness and stability of the solution for a class of dynamic systems describing chemical processes. Vestnic Moskovskogo Universiteta, Seriya, Comput. Math. Cybern., 4 (1977), 3-11. (in Russian).
• [12] A. Nemati and K. Mamehrashi: The use of the Ritz method and Laplace transform for solving 2D fractional-order optimal control problems described by the Roesser model. Asian Journal of Control, 21(3), (2019), 1189-1201. DOI: 10.1002/asjc.1791
• [13] R.A. Roesser: Discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, AC-20(1), (1975), 1-10. DOI: 10.1109/TAC.1975.1100844
• [14] K. Rogowski: General response formula for fractional 2D continuous-time linear systems described by the Roesser model. Acta Mechanica et Automatica, 5(2), (2011), 112-116.
• [15] A.N. Tikhonov and A.A. Samarski: Equations of Mathematical Physics. Science, Nauka, Moskva, 1972. (in Russian).