Control and Synchronization of a Memristor-based Hyperchaotic Lorenz System using Sliding Mode Control

Öz

We studied some new findings on the sliding mode control, that have been derived for the chaos synchronization of memristor – based hyperchaotic Lorenz systems. Nonlinear property has shown that the memristor can be used in chaotic circuits and the latest memristor-based chaotic circuits with different nonlinear equations at times its design attracts quite a lot of attention. The reason why the sliding mode control method is preferred is due to the fact that it is a robust approach and thus less susceptible to the external disturbances. In fact it is affected in a very little range. Numerical simulations of the synchronization of the proposed control methods with the studied system here, have proved to be largely valid.

Anahtar Kelimeler

• Memristor
• lorenz chaos system
• sliding mode control

Memristör Tabanlı Hiperkaotik Lorenz Sisteminin Kayan Kipli Kontrol Yöntemi Kullanılarak Senkronizasyonu ve Kontrolü

Öz

Bu çalışmada memristör tabanlı hiperkaotik lorenz sisteminin, dayanıklı doğrusal olmayan bir kontrol algoritması olan kayan kipli kontrol yöntemi kullanılarak senkronizasyonu ve kontrolü sağlanmıştır. Doğrusal olmayan özellik, memristörün kaotik devrelerde uygulanabileceğini göstermiş ve lineer olmayan denklemlere sahip farklı memristör tabanlı kaotik devreler, tasarımının oldukça fazla ilgi çektiği zamanlarda ortaya çıkmıştır. Bu çalışmada kayan kipli kontrol yönteminin tercih edilmesinin nedeni kayan kipli kontrolün sağlam bir yaklaşım olması, dış etkenlerden korunması ve çok az etkilenmesidir. Sayısal simülasyonlar, memristör tabanlı hiperkaotik lorenz sisteminin önerilen kayan kipli kontrol yöntemleriyle senkronizasyonunu doğrulamaktadır.

Anahtar Kelimeler

• Memristor
• lozenz chaos system
• sliding mode control

Kaynakça

1. [1] L. Chua, “Memristor-the missing circuit element,” IEEE Transactions on Circuit Theory, vol.18, no. 5, pp. 507-519, 1971. https://doi.org/10.1109/TCT.1971.1083337
2. [2] D. B. Strukov, G. S. Snider, D. R. Stewart, R. S. Williams, “The missing memristor found,” Nature, vol. 453, pp. 80–83, 2008. https://doi.org/ 10.1038/nature06932
3. [3] C. Yakopcic, R. Hasan, T. M. Taha, “Flexible memristor based neuromorphic system for implementing multi-layer neural network algorithms,” International Journal of Parallel, Emergent and Distributed Systems, vol. 33, no. 4, pp. 408–429, 2018. https://doi.org/10.1080/17445760.2017.1321761
4. [4] N. S. M. Hadis, A. A. Manaf, S. H. Ngalim, S. H. Herman, “Fabrication and characterisation of fluidic based memristor sensor for liquid with hydroxylgroup,” Sensing and Bio-Sensing Research, vo. 14, pp. 21–29, 2017. https://doi.org/10.1016/j.sbsr.2017.04.002
5. [5] G. Saha, R. Pasumarthy, P. Khatavkar, “Towards analog memristive controllers,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 62, no. 1, pp. 205– 214, 2015. http://doi.org/10.1109/TCSI.2014.2359715
6. [6] H. Kim, M. P. Sah, C. Yang, T. Roska, L. O. Chua, “Neural synaptic weighting with a pulse-based memristor circuit,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 1, pp. 148–158, 2012. http://doi.org/10.1109/TCSI.2011.2161360
7. [7] I. E. Ebong, P.Mazumder, “Self-controlled writing and erasing in a memristor crossbar memory,” IEEE Transactions on Nanotechnology, vol. 10, no. 6, pp. 1454–1463, 2011. http://doi.org/10.1109/TNANO.2011.2166805
8. [8]D. Varghese, G. Gandhi. “Memristor based high linear range differential pair, In Communications, Circuits and Systems,” ICCCAS 2009, International Conference on, IEEE, 2009, pp. 935–938.

9. [9]M. Itoh, L. Chua, “Memristor oscillators,” International Journal of Bifurcation and Chaos, vol. 18, no. 11, pp. 3183-3206, 2008. http://.doi.org/10.1142/S0218127408022354
10. [10]L. M. Pecora, T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, pp. 821-824, 1990. http://dx.doi.org/10.1103/PhysRevLett.64.821
11. [11]S. P. Wen, Z. G. Zeng, T. W. Huang, Y. R. Chen, “Fuzzy modeling and synchronization of different memristor-based chaotic circuits,” Physics Letters A, vol. 377, pp. 2016–2021, 2013. https://doi.org/10.1016/j.physleta.2013.05.046
12. [12]R. Yang, M. Wang, L. Li, Y. Zenggu, J. Jiang, “Integrated uncertainty/disturbance compensation with second-order sliding-mode observer for PMLSM-driven motion stage,” IEEE Transactions on Power Electronics, vol. 34, no. 3, pp. 2597–2607, 2018. https://doi.org/10.1109/TPEL.2018.2845705
13. [13]X. Sun, Z. Shi, L. Chen, Z. Yang, “Internal model control for a bearingless permanent magnet synchronous motor based on inverse system method,” IEEE Transactions on Energy Conversation, vol. 31, no. 4, pp. 1539–1548, 2016. https://doi.org/10.1109/TEC.2016.2591925
14. [14]U. E. Kocamaz, A. Goksu, H. Taskin, Y. Uyaroglu, “Synchronization of chaos in nonlinear finance system by means of sliding mode and passive control methods: A comparative study,” Information Technology and Control, vol. 44, no. 2, pp. 172–181, 2015. https://doi.org/10.5755/j01.itc.44.2.7732
15. [15]Y. Y. Hou, B. Y. Liau, H. C. Chen, “Synchronization of unified chaotic systems using sliding mode controller,” Mathematical Problems in Engineering, vol. 2012, pp. 10, 2012. https://doi.org/10.1155/2012/632712
16. [16]A. Gokyildirim, “A Novel Chaotic Attractor With a Line and Unstable Equilibria: Dynamics, Circuit Design, and Microcontroller-Based Sliding Mode Control,” IEEE Canadian Journal of Electrical and Computer Engineering, vol. 46, no.3, pp. 228-236, 2023. https://doi.org/10.1109/ICJECE.2023.3275281
17. [17]B. Cevher, T. E. Gumus, M. Turan, S. Emiroglu, M. A. Yalcin “A Single State Sliding Mode Controller Design Using Intelligent Optimization Algorithms for the Chaotic WINDMI System,” Tehnicki vjesnik, vol. 29, no. 2, pp. 504–510, 2022. https://doi.org/10.17559/TV-20201026120418
18. [18]A. Gokyildirim, H. Calgan, M. Demirtas, “Fractional-Order sliding mode control of a 4D memristive chaotic system,” Journal of Vibration and Control, vol. 30, no. 7-8, pp. 1604–1620, 2023. https://doi.org/10.1177/10775463231166187