Author:
Talbi Ibtissem,Ouannas Adel,Khennaoui Amina-Aicha,Berkane Abdelhak,Batiha Iqbal M.,Grassi Giuseppe,Pham Viet-Thanh
Abstract
Abstract
The paper investigates control and synchronization of fractional-order maps described by the Caputo h-difference operator. At first, two new fractional maps are introduced, i.e., the Two-Dimensional Fractional-order Lorenz Discrete System (2D-FoLDS) and Three-Dimensional Fractional-order Wang Discrete System (3D-FoWDS). Then, some novel theorems based on the Lyapunov approach are proved, with the aim of controlling and synchronizing the map dynamics. In particular, a new hybrid scheme is proposed, which enables synchronization to be achieved between a master system based on a 2D-FoLDS and a slave system based on a 3D-FoWDS. Simulation results are reported to highlight the effectiveness of the conceived approach.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference56 articles.
1. Diaz, J., Osler, T.: Differences of fractional order. Math. Comput. 28(125), 185–202 (1974)
2. Baleanu, D., Jajarmi, A., Asad, J.H., Blaszczyk, T.: The motion of a bead sliding on a wire in fractional sense (2017)
3. Jajarmi, A., Hajipour, M., Mohammadzadeh, E., Baleanu, D.: A new approach for the nonlinear fractional optimal control problems with external persistent disturbances. J. Franklin Inst. 355(9), 3938–3967 (2018)
4. Atici, F.M., Eloe, P.W.: A transform method in discrete fractional calculus. Int. J. Difference Equ. 2(2), 165–176 (2007)
5. Atici, F., Eloe, P.: Initial value problems in discrete fractional calculus. Proc. Am. Math. Soc. 137(3), 981–989 (2009)
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