Synchronization of an Extended Hyperchaotic Chen System with unknown parameters by Leveraging Adaptive Control
الموضوعات : Chaos Theory
Elahe Moradi
1
,
Hadi Soheili Rad
2
1 - Department of Electrical Engineering, YI.C., Islamic Azad University, Tehran, Iran.
2 - Department of Electrical Engineering, YI.C., Islamic Azad University, Tehran, Iran.
الکلمات المفتاحية: Adaptive Control, Chaos, Synchronization, Hyperchaotic Systems, Extended Chen System.,
ملخص المقالة :
In this study, an extended hyperchaotic Chen system is introduced. This system exhibits a significantly higher level of dynamical complexity compared to many conventional nonlinear systems. Such complexity broadens its potential for applications in secure communication systems and contributes to enhanced protection of sensitive information in networked environments. However, the system’s extreme sensitivity to parameter variations and initial conditions increases the risk of decoding errors. To address this challenge, the synchronization problem is investigated under the assumption of unknown parameters in the primary system. First, an effective adaptive control scheme is developed to estimate the system’s unknown parameters. Based on these estimated parameters, synchronization between master and slave systems is achieved. The stability of the proposed control strategy is established using Lyapunov theory, and simulation results substantiate its performance and reliability. Additionally, the hyperchaotic behavior of the proposed system is validated by calculating its Lyapunov exponents and performing dynamical analysis in MATLAB.
Z. Jing, D. Xu, Y. Chang, L. Chen, "Bifurcations, chaos, and system collapse in a three-node power system, " Electrical Power and Energy Systems, 25, 443-461, (2003), https://doi.org/10.1016/S0142-0615(02)00130-8. A. Cenys, A. Tamasevicius, A. Baziliauskas, R. Krivickas, E. Lindberg, "Hyperchaos in coupled Colpitts oscillators," Chaos, Solitons and Fractals, 17, 349-353, (2003), https://doi.org/10.1016/S0960-0779(02)00373-9. Z.-M. Ge, G.-H. Yang, "Hyperchaos of four state autonomous system with three positive Lyapunov exponents," Physics Letters A, 373 (3), 349-353, 2009, https://doi.org/10.1016/j.physleta.2008.11.046. E. Moradi, "Finite time stabilization of time-delay nonlinear systems with uncertainty and time-varying delay, " Journal of Control, 14(2), 79–87, (2020), https://doi.org/10.29252/joc.14.2.79. E. Moradi, M. R. Jahed-Motlagh, and M. B. Yazdi, "Delay-Dependent Finite-Time Stabilization of Uncertain Switched Time-Delay Systems with Norm-Bounded Disturbance," IETE Journal of Research, 64(2), 195–208, (2017), https://doi.org/10.1080/03772063.2017.1351898. N. Maleki and E. Moradi, "Robust H∞ Control of DC Motor in the Presence of Input Delay and Disturbance by the Predictor-Based Method," Complexity, 2022(1), (2022), https://doi.org/10.1155/2022/1902166. J. Li, J. Zheng, "Finite‑time synchronization of different dimensional chaotic systems with uncertain parameters and external disturbances," Scientific Reports, (2022), https://doi.org/10.1038/s41598-022-19659-7. W. Abbasi, Y-C. Liu, "Robust and resilient stabilization and tracking control for chaotic dynamical systems with uncertainties," International Journal of Dynamics and Control, (2021), https://doi.org/10.1007/s40435-021-00782-8. H. Su, R. Luo, J. Fu, M. Huang, "Fixed time control and synchronization of a class of uncertain chaotic systems with disturbances via passive control method," Mathematics and Computers in Simulation, 198, 474-493, (2022), https://doi.org/10.1016/j.matcom.2022.03.010. J.M. Munoz-Pacheco, C. Volos, F.E. Serrano, S. Jafari, J. Kengne, K. Rajagopal, "Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique," Entropy, 23, 921, 1-22, (2021), https://doi.org/10.3390/e23070921. Ashish, M. Sajid, "Stabilization in chaotic maps using hybrid chaos control procedure," Heliyon, 10, 1-16, (2024), https://doi.org/10.1016/j.heliyon.2024.e23984. Z. Liu, R. Guo, "Stabilization of a Class of Complex Chaotic Systems by the Dynamic Feedback Control," Complexity, 1-10, (2020), https://doi.org/10.1155/2020/4938149. W. Wu, Z. Chen, Z. Yuan, "The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos ," Chaos, Solitons and Fractals, 39 2340–2356, (2009), https://doi.org/10.1016/j.chaos.2007.07.016. Q. Jia, "Hyperchaos generated from the Lorenz chaotic system and its control," Physics Letters A, 366, 217-222, (2007), https://doi.org/10.1016/j.physleta.2007.02.024. O.E. ROSSLER, "AN EQUATION FOR HYPERCHAOS," PHYSICS LETTERS, 71A(2,3), 155-157, (1979), AN EQUATION FOR HYPERCHAOS. L. M. Tam, J. H. Chen, H. K. Chen, W. M. S Tou, "Generation of hyperchaos from the Chen–Lee system via sinusoidal perturbation," Chaos, Solitons and Fractals, 38, 826–839, (2008), https://doi.org/doi:10.1016/j.chaos.2007.01.039. K.-Y. Shao, A. Feng, T.-T. Wang, "Fixed-Time Sliding Mode Synchronization of Uncertain Fractional-Order Hyperchaotic Systems by Using a Novel Non-Singleton-Interval Type-2 Probabilistic Fuzzy Neural Network," Fractal Fract, 7, 247, 1-16, (2023), https://doi.org/10.3390/fractalfract7030247. Z. Chen, Y. Yang, G. Qi, Z. Yuan, "A novel hyperchaos system only with one equilibrium ," Physics Letters A, 360, 696–701, (2007), http://dx.doi.org/10.1016/j.physleta.2006.08.085. K. Benkouider, A. Sambas, T. Bonny, W.A. Nassan, I.A.R. Moghrabi, I.M. Sulaiman, B.A. Hassan, M. Mamat, "A comprehensive study of the novel 4D hyperchaotic system with self‑exited multistability and application in the voice encryption," Scientific Reports, 14, (2024), https://doi.org/10.1038/s41598-024-63779-1. Z. Bai, S. Li, H. Liu, X. Zhang, "Adaptive Fuzzy Backstepping Control of Fractional-Order Chaotic System Synchronization Using Event-Triggered Mechanism and Disturbance Observer," Fractal Fract, 6, 714, (2022), https://doi.org/10.3390/fractalfract6120714. F.-Q. Dou, J.-A. Sun, W.-S. Duan, K.-P. Lu, "Controlling hyperchaos in the new hyperchaotic system," Communications in Nonlinear Science and Numerical Simulation, 14, 552-559, (2009), https://doi.org/10.1016/j.cnsns.2007.10.009. H. Zhang, "An Integral Sliding Mode Control of Uncertain Chaotic Systems via Disturbance Observer," 2021, 1-11, (2021), https://doi.org/10.1155/2021/6628116. H. Tian, M. Zhao, J. Liu, Q. Wang, X. Yu, Z. Wang, "Dynamic Analysis and Sliding Mode Synchronization Control of Chaotic Systems with Conditional Symmetric Fractional-Order Memristors," Fractal Fract. 8, 307, (2024), https://doi.org/10.3390/fractalfract8060307. M. Zhao, J. Wang, "H_∞ control of a chaotic finance system in the presence of external disturbance and input time-delay," 233, 320-327, (2014), http://dx.doi.org/10.1016/j.amc.2013.12.085. E. Ozpolat, A. Gulten, "Synchronization and Application of a Novel Hyperchaotic System Based on Adaptive Observers," Appl. Sci. 2024, 14, 1311, 1-20, (2024), https://doi.org/10.3390/app14031311. Y. Ai, Z. Feng, H. Wang, "Fixed-Time Adaptive Fuzzy Anti-Synchronization Control of Hyperchaotic Rossler System Based on Backstepping Method," Int. J. Fuzzy Syst, 25(6), 2501–2513, (2023), https://doi.org/10.1007/s40815-023-01536-8. H.-T. Yau, J.-J. Yan, "Chaos synchronization of different chaotic systems subjected to input nonlinearity," Applied Mathematics and Computation, 197, 775–788, (2008), https://doi.org/10.1016/j.amc.2007.08.014. H.-T. Yau, J.-J. Yan, "Robust controlling hyperchaos of the Rossler system subject to input nonlinearities by using sliding mode control," Chaos, Solitons and Fractals, 33, 1767–1776, (2007), https://doi.org/10.1016/j.chaos.2006.03.016. L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems, "Physical Review Letters," 64(8), 821–824, (1990), https://doi.org/10.1103/physrevlett.64.821. C.-L. Kuo, C.-C. Wang, N.-S. Pai, "Design of Variable Structure Synchronization Controller for Two Different Hyperchaotic Systems Containing Nonlinear Inputs," Journal of Applied Sciences, 9(14), 2635-2639, (2009), https://doi.org/10.3923/jas.2009.2635.2639. H. Cheng, H. Li, Q. Dai, and J. Yang, "A deep reinforcement learning method to control chaos synchronization between two identical chaotic systems," Chaos Solitons & Fractals, 174, p. 113809, (2023), https://doi.org/10.1016/j.chaos.2023.113809.
