Synchronization of Uncertain Multiple Chaotic Systems Based on an Optimal Nonlinear Observer: A Secure Communication Approach

Authors

1 Graduated Master Degree, Faculty of Electical Engineering, Shahrood University of Technology, Shahrood, Iran.

2 Prof., Faculty of Electical Engineering, Shahrood University of Technology, Shahrood, Iran.

3 Faculty of Electical Engineering, Shahrood, Iran

10.22044/jsfm.2025.15688.3938

Abstract

In this paper, using an optimal observer-based super-twisting approach, a modified projective and transmission synchronization in the presence of uncertainty and disturbance signals is investigated for multiple chaotic systems involving one drive system and two response systems. First, in order to estimate the uncertain terms along with quickly deal with the disturbance signals, an optimal finite-time super-twisting observer is designed. Based on the Lyapunov stability theorem, a finite-time controller is then developed to ensure the chaos synchronization by converging observer error systems to zero. The proposed control law can be applied in chaotic secure communication systems to increase security. Additionally, we introduce the cascade inclusion method, which is more secure in comparison with previous approaches, for secure communication applications. Finally, the numerical simulations in comparison with related works are provided. The simulation results illustrate the robustness and effectiveness of the proposed control approach in the presence of uncertainty and disturbances.

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References

[1] Louis M (1992) Synchronization in chaotic systems, Phys Rev Lett  64(8): 821-825, 1990.
[2] Prliz U (1992) Experimental demonstration of secue Communication Via Chaotic synchronization, Int J Bifur Chaos 2(3): 709-713.
[3] Luo J, Qu S, Xiong Z, Appiagyei E (2019) Observer-based finite-time modified projective synchronization of multiple uncertain chaotic systems and applications to secure communication using DNA encoding. IEEE Access, 7: 65527-65543.
[4] Sudheesh KV (2022) Self-adaptive based medical image encryption using multiple chaotic systems. Int J Comput Appl 183(48): 0975-8887, 48.
[5] Wang X, Guan N, Zhao H, Wang S, Zhang Y (2020) Open a new image encryption scheme based on coupling map lattices with mixed multi-chaos. Sci Rep 10: 9784.
[6] Itong YLI, Ianguo JYU (2020) Multi scrolls chaotic encryption scheme for CO-OFDM-PON. Opt Express 28(14): 19808–19817.
[7] Chen X, Park JH, Cao J, Qiu J (2017) Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances, Appl Math Comput 308: 161–173.
[8] Chen X, Cao J, Qiu J, Alsaedi A, Alsaadi FE (2016) Adaptive control of multiple chaotic systems with unknown parameters in two different synchronization modes, Adv Differ Equ 2016: 1-17.
[9] Yadav N, Pallav, Handa H (2023) Projective synchronization for a new class of chaotic/hyperchaotic systems with and without parametric uncertainty. Trans Inst Meas Control 45(10): 1975-1985.
[10] Sun J, Shen Y, Zhang G, Sun J, Shen Y, Zhang G (2012) Transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control. Chaos: Interdiscip J Nonlinear Sci 22: 043107-1.
[11] Ahmad IA (2015) Research on the synchronization of two novel chaotic systems based on a nonlinear active control algorithm. Eng Technol Appl Sci Res 5(1): 739–747.
[12] Pahnehkolaei SMA, Alfi A, Machado JT (2020) Fuzzy logic embedding of fractional order sliding mode and state feedback controllers for synchronization of uncertain fractional chaotic systems. Comput Appl Math 39(3): 182.
[13] Tarammim A, Akter MTA (2022) Comparative study of synchronization methods of Rucklidge chaotic systems with design of active control and backstepping methods. Int J Mod Nonlinear Theory Appl. 11: 31–51.
[14] Akbar A, Javan K, Shoeibi A, Zare A, Izadi NH, Jafari M (2021) Design of adaptive-robust controller for multi-state synchronization of chaotic systems with unknown and time-varying delays and its application in secure communication. Sens 21(1): 254.
[15] Ahmad I, Shafiq M (2020) Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders. Automatika 61(3): 396–414.
[16] Behrooz F, Mariun N, Marhaban MH, Radzi MAM, Ramli AR (2018) Review of control techniques for HVAC systems-nonlinearity approaches based on fuzzy cognitive maps. Energies, 11(3): 495.
[17] Mobayen S (2018) Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control. ISA Trans 77: 100–111.
 
[18] Nabil H, Tayeb H (2025) Modified generalized projective synchronization of the geomagnetic Krause and Robert fractional-order chaotic system and its application in secure communication. Eur Phys J B, 98 (4): 56.
[19] Iqbal S, Wang J (2025) A novel fractional-order 3-D chaotic system and its application to secure communication based on chaos synchronization. Physica Scr 100(2): 025243.
[20] Strogatz SH, Oppenheim AV (1993) Synchronization of Lorenz-based chaotic circuits with applications to Communications. IEEE Trans Circuits and Sys II: Analog and Digital Signal Processing, 40(10): 626–633.
[21] Suchit S, Goenka P, Nand D (2024) Implementation of secure communication system using various chaotic systems, 3rd International Conference for Innovation in Technology, Bangalore, India, pp. 1-4.
[22] Bowong S, Kakmeni FMM, Siewe MS (2007) Secure communication via parameter modulation in a class of chaotic systems. Comm Nonlinear Sci Numer Simul 12(3): 397–410.
[23] L’Hernault, M, Barbot JP, Ouslimani A (2008) Feasibility of analog realization of a sliding-mode observer: Application to data transmission. IEEE Trans Circuits Syst I: Regular Papers 55(2): 614–624.
[24] Hong Y, Jiang ZP (2006) Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties,  IEEE Trans Autom Control 51(12): 1950-1956.
[25] Hong Y, Guowu Y, Linda B, Hua OW (2000) Global finite-time stabilization: from state feedback to output feedback. In Proceedings of the 39th IEEE Conference on Decision and Control, 3: 2908-2913.
[26] Sun K (2016) Chaotic secure communication: principles and technologies, Walter de Gruyter GmbH & Co KG.
[27] Short  KM (1994) Steps toward unmasking secure communications. Int. J. Bifur. Chaos, 4: 959–977.
[28] Chen G (2002) A new chaotic attractor coined, Int J Bifur Chaos 12(3): 659–661.
Journal of Solid and Fluid Mechanics
Volume 15, Issue 2
May and June 2025
Pages 17-32

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