Details
Title
Different linear control laws for fractional chaotic maps using Lyapunov functionalJournal title
Archives of Control SciencesYearbook
2021Volume
vol. 31Issue
No 4Authors
Affiliation
Almatroud, A. Othman : Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 81451, Saudi Arabia ; Ouannas, Adel : Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria ; Grassi, Giuseppe : Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy ; Batiha, Iqbal M. : Department of Mathematics, Faculty of Science and Information Technology, Irbid National University, Irbid, Jordan and Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE ; Gasri, Ahlem : Department of Mathematics, University of Larbi Tebessi, Tebessa 12002, Algeria ; Al-Sawalha, M. Mossa : Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 81451, Saudi ArabiaKeywords
discrete fractional calculus ; chaotic maps ; linear control ; Lyapunov methodDivisions of PAS
Nauki TechniczneCoverage
765-780Publisher
Committee of Automatic Control and Robotics PASBibliography
[1] C. Goodrich and A.C. Peterson: Discrete Fractional Calculus. Springer: Berlin, Germany, 2015, ISBN 978-3-319-79809-7.[2] P. Ostalczyk: Discrete Fractional Calculus: Applications in Control and Image Processing. World Scientific, 2016.
[3] K. Oprzedkiewicz and K. Dziedzic: Fractional discrete-continuous model of heat transfer process. Archives of Control Sciences, 31(2), (2021), 287– 306, DOI: 10.24425/acs.2021.137419.
[4] T. Kaczorek and A. Ruszewski: Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks. Archives of Control Sciences, 30(4), (2020), 667–681, DOI: 10.24425/acs.2020.135846.
[5] J.B. Diaz and T.J. Olser: Differences of fractional order. Mathematics of Computation, 28 (1974), 185–202, DOI: 10.1090/S0025-5718-1974-0346352-5.
[6] F.M. Atici and P.W. Eloe: A transform method in discrete fractional calculus. International Journal of Difference Equations, 2 (2007), 165–176.
[7] F.M. Atici and P.W. Eloe: Discrete fractional calculus with the nabla operator. Electronic Journal of Qualitative Theory of Differential Equations, Spec. Ed. I, 3 , (2009), 1–12.
[8] G. Anastassiou: Principles of delta fractional calculus on time scales and inequalities. Mathematical and Computer Modelling, 52(3-4), (2010), 556– 566, DOI: 10.1016/j.mcm.2010.03.055.
[9] T. Abdeljawad: On Riemann and Caputo fractional differences. Computers and Mathematics with Applications, 62(3), (2011), 1602–1611, DOI: 10.1016/j.camwa.2011.03.036.
[10] M. Edelman, E.E.N. Macau, and M.A.F. Sanjun (Eds.): Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives. Springer International Publishing, 2018.
[11] G.C. Wu, D. Baleanu, and S.D. Zeng: Discrete chaos in fractional sine and standard maps. Physics Letters A, 378(5-6), (2014), 484–487, DOI: 10.1016/j.physleta.2013.12.010.
[12] G.C. Wu and D. Baleanu: Discrete fractional logistic map and its chaos. Nonlinear Dynamics, 75(1-2), (2014), 283–287, DOI: 10.1007/s11071-013-1065-7.
[13] T. Hu: Discrete chaos in fractional Henon map. Applied Mathematics, 5(15), (2014), 2243–2248, DOI: 10.4236/am.2014.515218.
[14] G.C. Wu and D. Baleanu: Discrete chaos in fractional delayed logistic maps. Nonlinear Dynamics, 80 (2015), 1697–1703, DOI: 10.1007/s11071-014-1250-3.
[15] M.K. Shukla and B.B. Sharma: Investigation of chaos in fractional order generalized hyperchaotic Henon map. International Journal of Electronics and Communications, 78 (2017), 265–273, DOI: 10.1016/j.aeue.2017.05.009.
[16] A. Ouannas, A.A. Khennaoui, S. Bendoukha, and G. Grassi: On the dynamics and control of a fractional form of the discrete double scroll. International Journal of Bifurcation and Chaos, 29(6), (2019), DOI: 10.1142/S0218127419500780.
[17] L. Jouini, A. Ouannas, A.A. Khennaoui, X. Wang, G. Grassi, and V.T. Pham: The fractional form of a new three-dimensional generalized Henon map. Advances in Difference Equations, 122 (2019), DOI: 10.1186/s13662-019-2064-x.
[18] F. Hadjabi, A. Ouannas,N. Shawagfeh, A.A. Khennaoui, and G. Grassi: On two-dimensional fractional chaotic maps with symmetries. Symmetry, 12(5), (2020), DOI: 10.3390/sym12050756.
[19] D. Baleanu, G.C. Wu, Y.R. Bai, and F.L. Chen: Stability analysis of Caputo-like discrete fractional systems. Communications in Nonlinear Science and Numerical Simulation, 48 (2017), 520–530, DOI: 10.1016/j.cnsns.2017.01.002.
[20] A-A. Khennaoui, A. Ouannas, S. Bendoukha, G. Grassi, X. Wang, V-T. Pham, and F.E. Alsaadi: Chaos, control, and synchronization in some fractional-order difference equations. Advances in Difference Equations, 412 (2019), DOI: 10.1186/s13662-019-2343-6.
[21] A. Ouannas, A.A. Khennaoui, G. Grassi, and S. Bendoukha: On chaos in the fractional-order Grassi-Miller map and its control. Journal of Computational and Applied Mathematics, 358(2019), 293–305, DOI: 10.1016/j.cam.2019.03.031.
[22] A. Ouannas, A.A. Khennaoui, S. Momani, G. Grassi and V.T. Pham: Chaos and control of a three-dimensional fractional order discrete-time system with no equilibrium and its synchronization. AIP Advances, 10 (2020), DOI: 10.1063/5.0004884.
[23] A. Ouannas, A-A. Khennaoui, S. Momani, G. Grassi, V-T. Pham, R. El- Khazali, and D. Vo Hoang: A quadratic fractional map without equilibria: Bifurcation, 0–1 test, complexity, entropy, and control. Electronics, 9 (2020), DOI: 10.3390/electronics9050748.
[24] A. Ouannas, A-A. Khennaoui, S. Bendoukha, Z.Wang, and V-T. Pham: The dynamics and control of the fractional forms of some rational chaotic maps. Journal of Systems Science and Complexity, 33 (2020), 584–603, DOI: 10.1007/s11424-020-8326-6.
[25] A-A. Khennaoui, A. Ouannas, S. Bendoukha, G. Grassi, R.P. Lozi, and V-T. Pham: On fractional-order discrete-time systems: Chaos, stabilization and synchronization. Chaos, Solitons and Fractals, 119(C), (2019), 150– 162, DOI: 10.1016/j.chaos.2018.12.019.
[26] A. Ouannas, A-A. Khennaoui, Z. Odibat, V-T. Pham, and G. Grassi: On the dynamics, control and synchronization of fractional-order Ikeda map. Chaos, Solitons and Fractals, 123(C), (2015), 108–115, DOI: 10.1016/j.chaos.2019.04.002.
[27] A. Ouannas, F. Mesdoui, S. Momani, I. Batiha, and G. Grassi: Synchronization of FitzHugh-Nagumo reaction-diffusion systems via onedimensional linear control law. Archives of Control Sciences, 31(2), 2021, 333–345, DOI: 10.24425/acs.2021.137421.
[28] Y. Li, C. Sun, H. Ling, A. Lu, and Y. Liu: Oligopolies price game in fractional order system. Chaos, Solitons and Fractals, 132(C), (2020), DOI: 10.1016/j.chaos.2019.109583.
[29] D. Mozyrska and E. Girejko: Overview of fractional h-difference operators. In Advances in harmonic analysis and operator theory. Birkhäuser, Basel, 2013, 253–268.