• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology

Article

Indian Journal of Science and Technology

Year: 2020, Volume: 13, Issue: 20, Pages: 1977-1990

Original Article

Design of adaptive feedback control for new 3D chaotic system and its digital implementation on FPGA

Received Date:04 May 2020, Accepted Date:12 May 2020, Published Date:18 June 2020

Abstract

Background/Objectives : In this research work, digital circuit implementation on FPGA of an adaptive feedback control methodology for a new 3 – D chaotic system is proposed Methods/Statistical analysis: The chaos synchronization is achieved using adaptive feedback control method. The new adaptive controllers are designed to achieve the chaos synchronization for the identical new chaotic system. The FPGA implementation of chaos synchronization using numerical methods induces artificial suppression in the chaotic system or chaotic behavior can be dead in very short-time. In this research work, the FPGA implementation of chaos synchronization is achieved with the help of automatic code generator like System generator in Matlab simulink. The adaptive feedback control for identical new chaotic system is coded with VHDL with 32 bit fixed point number, 12 for the entire and 20 for the fraction. Findings: In this paper, we designed a new 3D chaotic system and its chaotic behavior is verified using Lyapunov exponents, stability analysis and Poincare map. The complete synchronization for proposed chaotic system is achieved using adaptive feedback control methodology. The digital circuit realization of adaptive feedback control for the synchronization of identical chaotic system based on FPGA is achieved for the various applications of digital information systems. Simulation results and FPGA outputs illustrate the effectiveness of our proposed method. Novelty/Applications: The digital implementation of adaptive feedback control has many engineering applications such as digital data transmission, digital modulation, video encryption, digital cryptosystem etc.

Keywords: Chaotic system; complete synchronization; adaptive feedback control; FPGA implementation; digital implementation

References

  1. Jafari S, Rajagopal K, Hayat T, Alsaedi A, Pham VT. Simplest Megastable Chaotic Oscillator. International Journal of Bifurcation and Chaos. 2019;29(13):1950187. doi: 10.1142/s0218127419501876
  2. Wang X, Yu J, Jin C, Ching H, Yu S. Chaotic oscillator based on memcapacitor and meminductor. Nonlinear Dynamics. 2019;96:161–173. Available from: https://doi.org/10.1007/s11071-019-04781-5
  3. Sun J, Yang Q, Wang Y. Dynamical analysis of novel memristor chaotic system and DNA encryption application. Iranian Journal of Science and Technology, Transactions of Electrical Engineers. 2020;44:449–460. Available from: https://doi.org/10.1007/s40998-019-00239-x
  4. Arab A, Rostami MJ, Ghavami B. An image encryption method based on chaos system and AES algorithm. The Journal of Supercomputing. 2019;75(10):6663–6682. doi: 10.1007/s11227-019-02878-7
  5. Singh PP, Roy BK. Microscopic chaos control of chemical reactor system using non linear active plus proportional integral sliding mode control techniques. The European Physical Journal Special Topics. 2019;228(1):169–184.
  6. Vaidhyanathan S, Boulkroune A. 2016. Available from: https://doi.org/10.1007/978-3-319-30279-9_19
  7. Cui S, Zhang J. Chaotic secure communication based on single feedback phase modulation and channel transmission. IEEE Photonics Journal. 2019;11(5):1–8.
  8. Wang DM, Wang LS, Guo YY, Wang YC, Wang AB. Key space enhancement of optical chaos secure communication: chirped FBG feedback semiconductor laser. Optics Express. 2019;27(3):3065. doi: 10.1364/oe.27.003065
  9. Vaidyanathan S. Adaptive control of the FitzHugh-Nagumo chaotic neuron model. International Journal of PharmTech Research. 2015;8(6):117–127.
  10. Vaidyanathan S. Adaptive chaotic synchronization of enzymes-substrates system with ferroelectric behaviour in brain waves. International Journal of PharmTech Research. 2015;8(5):964–973.
  11. Pecora LM, Carroll TL. Synchronization in chaotic systems. Physical Review Letters. 1990;64(8):821–824. doi: 10.1103/physrevlett.64.821
  12. Fang JS, Tsai JSH, Yan JJ, Guo SM. Adaptive Chattering-Free Sliding Mode Control of Chaotic Systems with Unknown Input Nonlinearity via Smooth Hyperbolic Tangent Function. Mathematical Problems in Engineering. 2019;2019:1–9. doi: 10.1155/2019/4509674
  13. Pérez-Cruz JH, Tamayo-Meza PA, Figueroa M, Silva-Ortigoza R, Ponce-Silva M, Rivera-Blas R, et al. Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control. Complexity. 2019;2019:1–10. doi: 10.1155/2019/4706491
  14. Khan A, Budhraja M, Ibraheem A. Synchronization Among Different Switches of Four Non-identical Chaotic Systems via Adaptive Control. Arabian Journal for Science and Engineering. 2019;44(3):2717–2728. doi: 10.1007/s13369-018-3458-x
  15. Vaidyanathan S, Abba O, Gambo B, Alidou M. A new three dimensional chaotic system: its adaptive control and circuit design. International Journal of Automation and Control. 2019;13(1):101–121.
  16. Hamed T. 2017. Available from: https://doi.org/10.1515/nleng-2017-0050
  17. Singh AK, Yadav VK, Das S. Synchronization of Time-delay Chaotic Systems with Uncertainties and External Disturbances. The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity. 2019;8(1):13–21. doi: 10.5890/dnc.2019.03.002
  18. Vaidyanathan S, Sampath S. Anti-synchronization of four-wing chaotic systems via sliding mode control. International Journal of Automation and Computing. 2012;9(3):274–279. doi: 10.1007/s11633-012-0644-2
  19. Vaidyanathan S. Synchronization of Tokamak systems with symmetric and magnetically confined plasma via adaptive control. International Journal of ChemTech Research. 2015;8(6):818–827.
  20. Vaidyanathan S. Adaptive biological control of generalized Lotka-Volterra three-species biological system. International Journal of PharmTech Research. 2015;8(4):622–631.
  21. Cun FF, Yan RT, Ying HW, Hai YY. Active backstepping control of projective synchronization among different non linear systems. Journal of Control, Measurements, Electronics, computing and communications. 2019;58:295–301.
  22. Eroglu D, Lamb JSW, Pereira T. Synchronisation of chaos and its applications. Informa UK Limited. 2017. doi: 10.1080/00107514.2017.1345844
  23. Chai X, Huigan Z. Function projective lag synchronization of chaotic systems with certain parameters via adaptive - impulsive control. International Journal of Automation and computing. 2019;16:238–247.
  24. Vaidyanathan S, Sambas A, Kacar S, Cavusoglu U. A New Finance Chaotic System, its Electronic Circuit Realization, Passivity based Synchronization and an Application to Voice Encryption. Nonlinear Engineering. 2019;8(1):193–205. doi: 10.1515/nleng-2018-0012
  25. Lee SH, Kapila V, Porfiri M, Panda A. Master–slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators. Communications in Nonlinear Science and Numerical Simulation. 2010;15(12):4100–4113. doi: 10.1016/j.cnsns.2010.01.035
  26. Pakiriswamy S. Active Controller Design for the Generalized Projective Synchronization Of Three-Scroll Chaotic Systems. International Journal of Advanced Information Technology. 2012;2(1):37–53. doi: 10.5121/ijait.2012.2104
  27. Sundarapandian V. Sliding mode controller design for global chaos synchronization of Rucklidge Chaotic Systems. International Journal on Bioinformatics and Biosciences. 2012;2(4):23–31.
  28. N, Quyen X, Kyamakya K. Springer. 2018. Available from: https://doi.org/10.1007/978-3-319-58996-1_11
  29. Bonilla LL, Alvaro M, Carretero M. Chaos-based true random number generators. Journal of Mathematics in Industry. 2016;7(1). doi: 10.1186/s13362-016-0026-4
  30. Lynnyk V, Sakamoto N, Čelikovský S. Pseudo random number generator based on the generalized Lorenz chaotic system. Elsevier BV. 2015. doi: 10.1016/j.ifacol.2015.11.046
  31. Guillén-Fernández O, Meléndez-Cano A, Tlelo-Cuautle E, Núñez-Pérez JC, Rangel-Magdaleno JdJ. On the synchronization techniques of chaotic oscillators and their FPGA-based implementation for secure image transmission. PLOS ONE. 2019;14(2):e0209618. doi: 10.1371/journal.pone.0209618
  32. Kingni ST, Rajagopal K, Kamdoum Tamba V, Ainamon C, Orou JBC. Analysis and FPGA implementation of an autonomous Josephson junction snap oscillator. The European Physical Journal B. 2019;92(10). doi: 10.1140/epjb/e2019-100304-x
  33. Pano-Azucena AD, Tlelo-Cuautle E, Rodriguez-Gomez G, de la Fraga LG. FPGA-based implementation of chaotic oscillators by applying the numerical method based on trigonometric polynomials. AIP Advances. 2018;8(7):075217. doi: 10.1063/1.5038583
  34. Rajagopal K, Kingni ST, Khalaf AJM, Shekofteh Y, Nazarimehr F. Coexistence of attractors in a simple chaotic oscillator with fractional-order-memristor component: analysis, FPGA implementation, chaos control and synchronization. Springer Science and Business Media LLC. 2019. doi: 10.1140/epjst/e2019-900001-8
  35. Rajagopal K, Guessas L, Vaidyanathan S, Karthikeyan A, Srinivasan A. 2017. Available from: https://doi.org/10.1155/2017/7307452

Copyright

© 2020 Rameshbabu, Suresh. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Published By Indian Society for Education and Environment (iSee)

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