Abstract
This paper proposes an adaptive controller for chaos synchronization using quantum neural networks (QNN). The main purpose is to design a communication system for transmission of information securely. In many applications of chaotic systems, the exact model of system is not available and may involve uncertainties such as external disturbance and parametric uncertainties originating from environmental conditions. To estimate the uncertainties in the receiver and improve the accuracy of synchronization and recovering the message signal for secure communication applications, a QNN is used. The parameters of the proposed system should be estimated by applying the adaptive rules obtained by Lyapunov theorem. Taylor series expansion has been utilized to obtain a linear relation between the output of quantum neural network and its adaptive parameters. Simulation results show that the synchronization procedure for state variables of the master and slave systems is performed well with negligible synchronization error. Also, its application is investigated in secure communication and cryptography.
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References
Ott E (2002) Chaos in dynamical systems. Cambridge University Press, Cambridge
Baranowski T (2006) Crisis and chaos in behavioral nutrition and physical activity. Int J Behav Nutr Phys Act 3(1):27
Ramachandran R, Samavedham L, Rangaiah GP (2005) "Investigating chaos in an industrial fluid catalytic cracking unit," in Proceedings of the 2005, American Control Conference, IEEE, pp. 3656–3658
Mikhailov AS, Showalter K (2006) Control of waves, patterns and turbulence in chemical systems. Phys Rep 425(2–3):79–194
Liu J, Xu R (2018) Adaptive synchronisation of memristor-based neural networks with leakage delays and applications in chaotic masking secure communication. Int J Syst Sci 49(6):1300–1315
Yang T (2004) A survey of chaotic secure communication systems. Int J Comput Cog 2(2):81–130
Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821
Huang C, Cao J (2017) Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system. Physica A 473:262–275
Mobayen S, Tchier F (2018) Synchronization of a class of uncertain chaotic systems with Lipschitz nonlinearities using state-feedback control design: a matrix inequality approach. As J Cont 20(1):71–85
Chen X, Park JH, Cao J, Qiu J (2018) Adaptive synchronization of multiple uncertain coupled chaotic systems via sliding mode control. Neurocomputing 273:9–21
Bouzeriba A, Boulkroune A, Bouden T (2016) Fuzzy adaptive synchronization of uncertain fractional-order chaotic systems. Int J Mach Learn Cybern 7(5):893–908
Khorashadizadeh S, Majidi M-H (2017) Chaos synchronization using the Fourier series expansion with application to secure communications. AEU-Int J Elect Comm 82:37–44
Khorashadizadeh S, Majidi M-H (2018) Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications. Front Inf Technol Elect Eng 19(9):1180–1190
Bagheri P, Shahrokhi M (2016) Neural network-based synchronization of uncertain chaotic systems with unknown states. Neural Comput Appl 27(4):945–952
Bigdeli N, Ziazi HA (2017) Design of fractional robust adaptive intelligent controller for uncertain fractional-order chaotic systems based on active control technique. Nonlinear Dyn 87(3):1703–1719
Åström KJ, McAvoy TJ (1992) Intelligent control. J Process Control 2(3):115–127
Aleksendrić D, Jakovljević Ž, Ćirović V (2012) Intelligent control of braking process. Expert Syst Appl 39(14):11758–11765
Jeswal S, Chakraverty S (2019) Recent developments and applications in quantum neural network: a review. Arch Comp Meth Eng 26(4):793–807
Zhu DQ, Sang QB (2006) "Fault diagnosis algorithm for the photovoltaic radar electronic equipment based on quantum neural networks," Dianzi Xuebao(Acta Electronica Sinica), vol. 34, no. 3, pp. 573–576
Li F, Xie C, Zheng D, Zheng B (2006) "Feedback quantum neuron for multiuser detection," in The 2006 IEEE International Joint Conference on Neural Network Proceedings, IEEE, pp. 2967–2971
Hu S (2004) Quantum neural network for image watermarking. International symposium on neural networks. Springer, pp 669–674
He W, Luo T, Tang Y, Du W, Tian YC, Qian F (2019) Secure communication based on quantized synchronization of chaotic neural networks under an event-triggered strategy. IEEE Trans Neural Netw Learn Syst 31(9):3334–3345
Mobini M, Kaddoum G (2020) Deep chaos synchronization. IEEE Open J Comm Soc 1:1571–1582
Shanmugam L, Mani P, Rajan R, Joo YH (2018) Adaptive synchronization of reaction–diffusion neural networks and its application to secure communication. IEEE Trans Cybernet 50(3):911–922
Ouyang D, Shao J, Jiang H, Nguang SK, Shen HT (2020) Impulsive synchronization of coupled delayed neural networks with actuator saturation and its application to image encryption. Neural Netw 128:158–171
Gupta M, Gupta M, Deshmukh M (2020) Single secret image sharing scheme using neural cryptography. Multim Tools Appl. https://doi.org/10.1007/s11042-019-08454-8
Xiu C, Zhou R, Liu Y (2020) New chaotic memristive cellular neural network and its application in secure communication system. Chaos Sol Fract, 141, 110316
Chen L, Yin H, Huang T, Yuan L, Zheng S, Yin L (2020) Chaos in fractional-order discrete neural networks with application to image encryption. Neural Netw 125:174–184
Shahnazi R, Shanechi H, Pariz N (2006) "Position control of induction and DC servomotors: a novel adaptive fuzzy PI sliding mode control," in 2006 IEEE Power Engineering Society General Meeting, IEEE, p. 9 pp
Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257
Addeh A, Khormali A, Golilarz NA (2018) Control chart pattern recognition using RBF neural network with new training algorithm and practical features. ISA Trans 79:202–216
Zhang W (2017) Research on computer digital signal processing network based on the RBF neural network. J Elect Syst 7(3):67
Sadiq A, Ibrahim MS, Usman M, Zubair M, Khan S (2018) "Chaotic time series prediction using spatio-temporal rbf neural networks," in 2018 3rd International Conference on Emerging Trends in Engineering, Sciences and Technology (ICEEST), IEEE, pp. 1–5
Chen S, Billings S (1992) Neural networks for nonlinear dynamic system modelling and identification. Int J Control 56(2):319–346
Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20(2):130–141
Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifur Chaos 9(07):1465–1466
Matsui N, Takai M, Nishimura H (2000) "A network model based on qubitlike neuron corresponding to quantum circuit," Electronics and Communications in Japan (Part III: Fundamental Electronic Science), vol. 83, no. 10, pp. 67–73
Salahshour E, Malekzadeh M, Gholipour R, Khorashadizadeh S (2019) Designing multi-layer quantum neural network controller for chaos control of rod-type plasma torch system using improved particle swarm optimization. Evol Syst 10(3):317–331
Slotine JJE, Li W (1991) Applied nonlinear control (no. 1). Prentice hall Englewood Cliffs, NJ
Samimi M, Majidi MH, Khorashadizadeh S (2021) "Secure communication based on chaos synchronization using brain emotional learning," AEU-Int J Elect Comm, 127, 153424
Fateh MM, Ahmadi SM, Khorashadizadeh S (2014) Adaptive RBF network control for robot manipulators. J AI Data Min 2(2):159–166
Izadbakhsh A, Kalat AA, Khorashadizadeh S (2021) "Observer-based adaptive control for HIV infection therapy using the Baskakov operator," Biomed Sig Proc Cont, vol. 65, 102343
Liao T-L, Tsai S-H (2000) Adaptive synchronization of chaotic systems and its application to secure communications. Chaos, Sol Fract 11(9):1387–1396
Yang T, Wu CW, Chua LO (1997) Cryptography based on chaotic systems. IEEE Trans Circ Syst I Fund Theory Appl 44(5):469–472
Majidi MH, Khorashadizadeh S (2020) Chaos synchronization using differential equations and the universal approximation theorem with application to secure communication and cryptography. J Elect Cyber Def 5(420):17–27
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Aliabadi, F., Majidi, MH. & Khorashadizadeh, S. Chaos synchronization using adaptive quantum neural networks and its application in secure communication and cryptography. Neural Comput & Applic 34, 6521–6533 (2022). https://doi.org/10.1007/s00521-021-06768-z
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DOI: https://doi.org/10.1007/s00521-021-06768-z