Abstract

In this paper, a new suitable adaptive controller is developed to realize a general method for hybrid projective combination synchronization (HPCS)of a class of fractional-order chaotic systems. Firstly, the definition of HPCS of fractional-order uncertain chaotic systems with external disturbance is introduced. Secondly, based on fractional Lyapunov's direct method an adaptive control and parameter adaptive laws are designed to achieve HPCS of uncertain chaotic systems. Finally, a numerical example is carried out to verify the effectiveness of the proposed methods.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 4
Year: 2023

DOI: 10.12732/ijam.v36i4.6

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References

1. [1] N. Aguila-Camacho, M.A. Duarte-Mermoud and J. Gallegos, A Lyapunov function for fractional order systems, Communications in Nonlinear Science and Numerical Simulation, 19 (2014), 2951-2957.
2. [2] F. Badri, and M. Sojoodi, Robust stabilisation of fractional-order interval systems via dynamic output feedback: An LMI approach, International Journal of Systems Science, 50 (2019), 1718-1730.
3. [3] S. Dadras and H.R. Momeni, Control of a fractional-order economical system via sliding mode, Physica A, 389 (2010), 2434-2442.
4. [4] K. Diethelm, N.J. Ford and A.D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynamics, 29 (2002), 3-22.
5. [5] C. Jiang, S. Liu and D. Wang, Generalized combination complex synchronization for fractional-order chaotic complex systems, Entropy, 17 (2015), 5199-5217.
6. [6] S. Kaouache, Projective synchronization of the modified fractional-order hyperchaotic rossler system and its application in secure communication, Universal Journal of Mathematics and Applications, 4 (2021), 50-58.
7. [7] S. Kaouache and T. Bouden, Modified hybrid synchronization of identical fractional hyperchaotic systems with incommensurate order, Dynamics of Continuous, Discrete and Impulsive Systems. Serie A: Mathematical Analysis, 28 (2021), 25-36.
8. [8] S. Kaouache, M.S. Abdelouahab and N.D. Hamri, Generalized combination synchronization of three different dimensional fractional chaotic and hyperchaotic systems using three scaling matrices, Journal of Advanced Research in Dynamycal and Control Systems, 212 (2020), 330-337.
9. [9] S. Kaouache and M.S. Abdelouahab, Inverse matrix projective synchronization of novel hyperchaotic system with hyperbolic sine function nonlinearity, Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications and Algorithms, 27 (2020), 145-154.
10. [10] S. Kaouache and M.S. Abdelouahab, Generalized synchronization between two chaotic fractional non-commensurate order systems with different dimensions, Nonlinear Dynamics and Systems Theory, 18 (2018), 273-284.
11. [11] S. Kaouache and M.D. Abdelouahab, Modified projective synchronization between integer order and fractional order hyperchaotic systems, Journal of Advanced Research in Dynamycal and Control Systems, 10 (2018), 96- 104.
12. [12] B. Labed, S. Kaouache and M.S. Abdelouahab, Control of a novel class of uncertain fractional-order hyperchaotic systems with external disturbances via sliding mode controller, Nonlinear Dynamics and Systems Theory, 20 (2020), 203-213.
13. [13] Q. Li, B. Shen, J. Liang and H. Shu, Event-triggered synchronization control for complex networks with uncertain inner coupling, International Journal of General Systems, 44 (2015), 212-225.
14. [14] R. Luo, Y. Wang and S. Deng, Combination synchronization of three classic chaotic systems using active backstepping design, Chaos, 21 (2011), Art. 043114.
15. [15] D. Matignon, Stability results for fractional differential equations with applications to control processing, Computing Eng. Syst. Appl., 2 (1996), 963-968.
16. [16] N. Noghredani and S. Balochian, Synchronization of fractional-order uncertain chaotic systems with input nonlinearity, International Journal of General Systems, 44 (2015), 485-498.
17. [17] X.W. Wang and M.J. Wang, Chaos control of a fractional-order modified coupled dynamos system, Nonlinear Analysis: Theory, Methods and applications, 71 (2009), 6126-6134.
18. [18] K. Xi, Y. Li and X. Huang, Adaptive function projective combination synchronization of three different fractional order chaotic systems, Optik, 26 (2015), 5346-5349.