سنکرونسازی آشوب براساس معادلات دیفرانسیل و قضیه تقریب عمومی و کاربرد آن در مخابرات امن و رمزنگاری

نویسندگان

بیرجند

چکیده

در این مقاله، یک روش جدید به‌منظور سنکرون‌سازی آشوب با استفاده از کنترل غیرخطی ارائه شده است. در اکثر کنترل-کننده‌های موجود فرض می‌شود مدل ریاضی سیستم‌های آشوبی فرستنده و گیرنده کاملاً یکسان هستند. با توجه به یکسان‌نبودن شرایط محیطی فرستنده و گیرنده و تاثیر درجه حرارت و سایر عوامل بر پارامترهای سیستم آشوبی از قبیل مقادیر مقاومت‌ها و سایر المان‌ها، یکسان درنظرگرفتن مدل‌های فرستنده و گیرنده معقول نیست. در این مقاله، روش جدیدی برای تخمین عدم قطعیت‌ها ارائه شده است که در آن عدم قطعیت‌ها با یک معادله دیفرانسیل خطی با ضرایب نامعلوم ثابت مدل‌سازی می‌شود. به عبارت دیگر، عدم قطعیت‌ها را می‌توان به‌صورت پاسخ این معادله دیفرانسیل نمایش داد. با توجه به این‌که این تابع (پاسخ معادله دیفرانسیل) شرایط قضیه تقریب عمومی را دارد، می‌توان هر تابع غیرخطی را با دقت دلخواه تخمین زد، اما با توجه به این‌که ضرایب معادله دیفرانسیل نامعلوم می‌باشند، پارامترهای این تابع نیز نامعلوم بوده و باید تخمین زده شوند. این‌کار با استفاده از قوانین تطبیق به‌دست‌آمده از تحلیل همگرایی خطای سنکرون‌سازی انجام می‌‌گردد. نتایج شبیه‌سازی بیانگر عملکرد مناسب تخمین‌گر ارائه شده بوده و در مقایسه با کنترل‌کننده فازی مد لغزشی سرعت پاسخ کنترل‌کننده پیشنهادی بهتر می‌باشد. همچنین، کاربرد آن در مخابرات امن و رمزنگاری مورد بررسی قرار گرفته است.

کلیدواژه‌ها

مراجع

  1. L. Kocarev, G. Jakimoski, T. Stojanovski, and U. Parlitz, “From Chaotic Maps to Encryption Schemes.” In Proceedings IEEE International Symposium Circuits and Systems, vol. 4, pp. 514-517, 1998.
  2. B. Fathi Vajargah, R. Asghari, and J. Vahidi, “Design and Analysis of a Novel Synchronous Stream Cipher Using Secure Pseudo Random Number Generator.” Journal of Electronical & Cyber Defence, vol. 4, no. 1, pp. 59-68, 2016 (in Persian).
  3. A. Mirghadri, and A. Jolfaei, “A Novel Image Encryption Scheme Using Chaotic Maps.” Passive Defence Sci. & Tech., vol. 2, no. 2, pp. 111-124, 2011 (in Persian).
  4. L. M. Pecora and T. L. Carroll, “Synchronization in Chaotic Systems,” Phys. Rev. Lett., vol. 64, pp. 821-824, 1990.
  5. K. Y. Lian, P. Liu, and T.S. Chiang, “Adaptive Synchronization Design for Chaotic Systems via a Scalar Driving Signal.” IEEE Trans. Circuits-I, vol .49, pp. 17-27, 2002.
  6. K. S. Halle, C. W. Wu, M. Itoh, and L. O. Chua, “Spread Spectrum Communication Through Modulation of Chaos”, Int. J. Bifurcat Chaos, vol .3 , pp. 469-477, 1993.
  7. T. L. Liao, and N. S. Huang, “An Observer-Based Approach for Chaotic Synchronization with Application to Secure Communication”, IEEE Trans. Circuits-I, vol .46, pp. 1144-1150, 1999.
  8. G. Kolumban, M. P. Kennedy, and L. O. Chua, “The Role of Synchronization in Digital Communication Using Chaos—Part I: Fundamentals of Digital Communications.”, IEEE Trans. Circuits-I, vol .44, pp.927-936, 1997.
  9. K. Murali, H. Yu, V. Varadan, and H. Leung, “Secure Communication Using a Chaos Based Signal Encryption Scheme.” IEEE Trans. Consum Electr, vol .47, pp. 709-714, 2001.
  10. J. M. V. Grzybowski, M. Rafikov and J. M. Balthazar, “Synchronization of the unified chaotic system and application in secure communication”, Commun. Nonlinear Sci. Numer. Simul. vol. 14, pp. 2793-2806, 2009.
  11. C. Yin, S. M. Zhong, and W. F. Chen, “Design PD controller for master–slave synchronization of chaotic Lur’e systems with sector and slope restricted nonlinearities,” Commun. Nonlinear Sci. Numer. Simul., vol. 16, pp. 1632–1639, 2011.
  12. J. S. Lin, and J. J. Yan, “Adaptive synchronization for two
  13. identical generalized Lorenz chaotic systems via a single controller.” Nonlinear Anal. Real World Appl., vol. 10, pp. 1151–1159, 2009.
  14. M. Pourmahmood, S. Khanmohammadi, and G. Alizadeh, “Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller.” Commun. Nonlinear Sci. Numer. Simul. vol. 16, pp. 2853–2868, 2011.
  15. L. Li, Y. Liu, and Q. J. Yao, “Robust synchronization of chaotic systems using sliding mode and feedback control,” Zhejiang Univ. - Sci. C, vol. 15, pp. 211-222, 2014.
  16. L. Xiao-run, Z. Liao-ying, and Z. Guang-zhou, “Sliding mode control for synchronization of chaotic systems with structure or
  17. parameters mismatching.” J. Zheijang Univ.-Sci. A, vol. 6, pp. 571-576, 2005.
  18. W. Jing, T. Zhen-Yu, M. Xi-Kui, and G. Jin-Feng, “A novel adaptive observer-based control scheme for synchronization and suppression of a class of uncertain chaotic systems,”
  19. Chinese Physics Letters, vol. 26, no. 5, pp. 050503, 2009.
  20. J. Yang, Y. Chen, and F. Zhu, “Associated observer-based synchronization for uncertain chaotic systems subject to channel noise and chaos-based secure communication,” Neurocomputing, vol. 167, pp. 587-595, 2015.
  21. P. Bagheri, M. Shahrokhi, and H. Salarieh, “Adaptive observer-based synchronization of two non-identical chaotic systems with unknown parameters,” J. Vib. Control, vol. 23, pp. 389-399, 2017.
  22. E. Cherrier, M. Boutayeb, and J. Ragot, “Observers-based synchronization and input recovery for a class of nonlinear chaotic models”, IEEE Trans. Circ Syst – Part I, vol. 53, pp. 1977-1988, 2006.
  23. M. Feki, “An adaptive chaos synchronization scheme applied to secure communication,” Chaos, Solitons and Fractals, vol. 18, pp. 141–148, 2003.
  24. J. Yang, Y. Chen, and F. Zhu, “Singular reduced-order observer-based synchronization for uncertain chaotic systems subject to channel disturbance and chaos-based secure communication,” Appl. Math. Comput., vol. 229, pp. 227–238, 2014.
  25. M. Chen, D. Zhou, and Y. Shang, “A sliding mode observer based secure communication scheme,” Chaos Soliton Fract., vol. 25, pp. 573–578, 2005.
  26. C. F. Hsu, “Adaptive fuzzy wavelet neural controller design for chaos synchronization,” Exp. Syst. Appl., vol. 38, pp. 10475–10483, 2011.
  27. C. S. Chen, “Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems,” Exp. Syst. Appl., vol. 36, pp. 11827–11835, 2009.
  28. T. C. Lin, F. Y. Huang, Z. Du, and Y. C. Lin, “Synchronization of fuzzy modeling chaotic time delay memristor-based Chua’s circuits with application to secure communication,” International Journal of Fuzzy Systems, vol. 17, no. 2, pp. 206-214, 2015.
  29. C. Mou, C. S. Jiang, J. Bin, and Q. X. Wu, “Sliding mode synchronization controller design with neural network for uncertain chaotic systems,” Chaos Soliton Fract., vol. 39, pp. 1856–1863, 2009.
  30. S. Khorashadizadeh and M. M. Fateh, “Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion,” Robotica, vol. 35, no. 2, pp. 310-336, 2015.
  31. L. X. Wang, “A Course in Fuzzy Systems and Control,” Prentice-Hall, New York, 1997.
  32. M. Gupta, L. Jin, and N. Homma, “Static and dynamic neural networks: from fundamentals to advanced theory,” John Wiley & Sons, 2004.
  33. M. M. Fateh, S. Azargoshasb, and S. Khorashadizadeh, “Model-free discrete control for robot manipulators using a fuzzy estimator,” COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33, no. 3, pp. 1051-1067, 2014.
  34. M. M. Fateh, S. M. Ahmadi, and S. Khorashadizadeh, “Adaptive RBF network control for robot manipulators.” Journal of AI and Data Mining, vol. 2, no. 2, pp. 159-166, 2014.
  35. S. Khorashadizadeh and M. M. Fateh, “Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation,” Nonlinear Dyn., vol. 79, no. 2, pp. 1151-1161, 2015.
  36. M. M. Fateh and S. Khorashadizadeh, “Optimal Robust voltage control of electrically driven robots,” Nonlinear Dyn., vol. 70, no. 2, pp. 1445–1458, 2012.
  37. A. C. Huang, S. C. Wu, and W. F. Ting, “A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments,” Robotica, vol. 24, no. 2, pp. 205-210, 2006.
  38. K. Chen-Yu and A. C. Huang, “A regressor-free adaptive controller for robot manipulators without Slotine and Li's modification,” Robotica, vol. 31, no. 7, pp. 1051-1058, 2013.
  39. C. Ming-Chih and A. C. Huang, “Adaptive impedance controller design for flexible-joint electrically-driven robots without computation of the regressor matrix,” Robotica, vol. 30, no. 1, pp. 133-144, 2012.
  40. M. B. Fard and S. Khorashadizadeh, “Model free robust impedance control of robot manipulators using fourier series expansion,” In AI & Robotics (IRANOPEN), IEEE 2015, pp. 1-7, 2015.
  41. S. Khorashadizadeh and M. M. Fateh, “Adaptive Fourier series-based control of electrically driven robot manipulators,” The 3rd International Conference on Control, Instrumentation and Automation (ICCIA), IEEE, pp. 213-218, 2013.
  42. A. Izadbakhsh, and S. Khorashadizadeh, “Robust task-space control of robot manipulators using differential equations for uncertainty estimation,” Robotica, vol. 35, no. 9, pp. 1923-1938, 2017.
  43. J. Effa, B. Essimbi, and J. Ngundam, “Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control,” Nonlinear Dyn., vol. 58, no. 1, pp. 39-47, 2009.
  44. J. J. Slotine and W. Li, “Applied nonlinear control,” Englewood Cliffs, NJ: prentice-Hall, 1991.
  45. C. L. Kuo, “Design of a fuzzy sliding-mode synchronization controller for two different chaos systems,” Computers and Mathematics with Applications, vol. 61, pp. 2090–2095, 2011.
  46. M. M. Fateh and S. Khorashadizadeh, “Robust control of electrically driven robots by adaptive fuzzy estimation of uncertainty,” Nonlinear Dynamics, vol. 69, no. 3, pp. 1465-1477, 2012.
  47. G. Grassi, and S. Mascolo, “Synchronizing Hyperchaotic Systems by Observer Design,” IEEE Trans. Circuits-II, vol. 46, no. 4, pp. 478-483, 1999.
  48. S. Khorashadizadeh and M. H. Majidi, “Chaos synchronization using the Fourier series expansion with application to secure communications,” AEU-INT J ELECTRON C, vol. 82, pp. 37-44, 2017.
  49. S. Khorashadizadeh and M. H. Majidi, “Synchronization of two different chaotic systems using Legendre polynomials with application to secure communications,” FRONT INFORM TECHEL, 2018. [doi="10.1631/FITEE.1601814"]
  50. T. Yang, C. W. Wu, and O. Chua, “Cryptography based on chaotic systems,” IEEE Trans. Circuits-I, vol. 44, no. 5, pp. 469-471, 1997.

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سابقه مقاله

  • تاریخ دریافت: 20 دی 1395
  • تاریخ بازنگری:
  • تاریخ پذیرش: 28 شهریور 1397
  • تاریخ انتشار: 10 دی 1396

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