Araştırma Makalesi
BibTex RIS Kaynak Göster

Zaman Gecikmeli Diferansiyel Denklem Tabanlı Kaotik Sistemlerde Çevrimiçi Zaman Gecikmesi Kestirimi

Yıl 2017, Cilt: 3 Sayı: 3, 65 - 73, 27.12.2017

Öz

Bu çalışmada, gecikmeli fark denklemleri tabanlı kaotik sistemlerde zaman gecikmesi kestirimi ele alınmıştır. Zaman gecikmesi, sistemin doğrusallığını bozan bir parametre olarak düşünülmüştür. Bu düşünce doğrultusunda, doğrusal olmayan bir kestirim yönteminden faydalanılmıştır. Bu yöntem, Lyapunov kararlılık analizlerine dayanmaktadır ve tüm sinyallerin küresel olarak sınırlı kalmasını ve kestirim hatasının sıfıra yakın bir noktaya yakınsamasını garanti etmektedir. Zaman gecikmesi kestirimi yönteminin etkinliğini göstermek için, birbirinden farklı, gecikmeli fark denklemleri tabanlı kaotik sistem modelleri kullanılarak birden fazla sayısal benzetim çalışmaları yapılmıştır. Sayısal benzetim çalışmaları sonucunda, yöntemin etkili bir şekilde çalıştığı görülmüştür.

Kaynakça

  • [1] Pecora L. and Carroll T. 1990. Synchronization in chaotic systems. Physical Review Letters, 64, 821- 823.
  • [2] Pecora L. and Carroll T. 1991. Driving systems with chaotic signals. Physical Review Letters, 44, 2374-2383.
  • [3] Kocarev L., Hall K. S., Eckert K., Chua L. O., and Parlitz U. 1992. Experimental demonstration of secure communications via chaotic synchronization. Int. J. of Bifurcation and Chaos, 2(3), 709-713.
  • [4] Cuomo K. M. and Oppenheim A. V. 1993. Circuit implementation of synchronized chaos with applications to communication. Physical Review Letters, 71, 65-68.
  • [5] Richard J.-P. 2003. Time-delay systems: an overview of some recent advances and open problems. Automatica, 39(10), 1667-1694.
  • [6] Banerjee S. 2009. Synchronization of timedelayed systems with chaotic modulation and cryptography. Chaos, Solitons & Fractals, 42(2), 745-750.
  • [7] Udaltsov V. S., Goedgebuer J.-P., Larger L., Cuenot J.-B., Levy P., and Rhodes W. T. 2003. Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations. Physics Letters A, 308(1), 54-60.
  • [8] Udaltsov V. S., Larger L., Goedgebuer J. P., Locquet A. and Citrin D. S. 2005. Time delay identification in chaotic cryptosystems ruled by delay-differential equations. J. of Optical Technology, 72, 373-377.
  • [9] Tang Y., Cui M., Li L., Peng H. and Guan X. 2009. Parameter identification of time-delay chaotic system using chaotic ant swarm. Chaos, Solitons & Fractals, 41(4), 2097-2102.
  • [10] Banerjee S., Ghosh D., Ray A. and Chowdhury R. 2008. Synchronization between two different time-delayed systems and image encryption. A letter Journal Exploring the frontiers physics, 81(2), 1-6.
  • [11] Yalcin M. E. and Ozoguz S. 2007. n-scroll chaotic attractors from a first-order time-delay differential equation. American Institute of Physics, 17(033112), 1-8.
  • [12] Uçar A. and Bishop S.R. 2001. Chaotic behaviour in a nonlinear delay system. Int. J. of Nonlinear Sciences and Numerical Simulation, 2(3), 289-294.
  • [13] Ucar A. 2002. A prototype model for chaos studies. Int. J. Eng. Sci., 40(5), 251-258.
  • [14] Ucar A. 2003. On the chaotic behaviour of prototype delayed dynamical system. Chaos, Solitons & Fractals, 16(2), 187-194.
  • [15] Lu H. and He Z. 1996. Chaotic behavior in firstorder autonomous continuous-time systems with delay. IEEE Tr. on Circuits and Systems-I: Fundamental Theory and Applications, 43(8), 700- 702.
  • [16] Wang L. and Yang X. 2006. Generation of multi–scroll delayed chaotic oscillator. Electronics Letters, 42(25), 1439-1441.
  • [17] Mackey M. C. and Glass L. 1977. Oscillation and chaos in physiological control systems. Science, 197(4300), 287-289.
  • [18] Glass L., Beuter A. and Larocque D. 1988. Time delays, oscillations, and chaos in physiological control systems. Mathematical Biosciences, 90, 111- 125.
  • [19] Namajunas A., Pyragas K. and Tamasevicius A. 1995. An electronic analog of the Mackey–Glass system. Physics Letters A, 201, 42-46.
  • [20] Glass L. 2001. Synchronization and rhythmic processes in physiology. Nature, 410, 277-284.
  • [21] Tian Y.-C. and Gao F. 1998. Adaptive control of chaotic continuous-time systems with delay. Physica D, 117, 1-12.
  • [22] Wang H., Wang X., Zhu X.-J., Wang X.-H. 2012. Linear feedback controller design method for time-delay chaotic systems. Nonlinear Dynamics, 70(1), 355–362.
  • [23] Ponomarenko V. I. and Prokhorov M. D. 2002. Extracting information masked by the chaotic signal of a time-delay system. Physical Review E, 66, 1-7.
  • [24] Zhou C. and Lai C. H. 1999. Extracting messages masked by chaotic signals of time-delay systems. Physical Review E, 60, 1-4.
  • [25] Prokhorov M. D., Ponomarenko V. I., Karavaev A. S. and Bezruchko B. P. 2005. Reconstruction of time-delayed feedback systems from time series. Physica D: Nonlinear Phenomena, 203(3-4), 209- 223.
  • [26] Banerjee T., Biswas D. and Sarkar B. 2013. Anticipatory, complete and lag synchronization of chaos and hyperchaos in a nonlinear delay-coupled time-delayed system. Nonlinear Dynamics, 72(1-2), 321-332.
  • [27] Chen D., Zhang R., Ma X. and Liu S. 2012. Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme. Nonlinear Dynamics, 69(1-2), 35-55.
  • [28] Mensour B. and Longtin A. 1998. Synchronization of delay-differential equations with application to private communication. Physics Letters A, 244, 59-70.
  • [29] Beheshti S. and Khaloozadeh H. 2013. Synchronization of chaotic systems with unknown time delay by sliding mode observer approach and unknown delay identification. in Iranian Conf. on Electrical Eng., 14-16 May. Mashhad, Iran, 1-6.
  • [30] Ambika G. and Amritkar R. E. 2011. Delay or anticipatory synchronization in one-way coupled systems using variable delay with reset. Pramana - J. of Physics, 77(5), 891-904.
  • [31] Tang Y. and Guan X. 2009. Parameter estimation of chaotic system with time-delay: A differential evolution approach. Chaos, Solitons & Fractals, 42(5), 3132-3139.
  • [32] Lin J. 2014. Parameter estimation for time-delay chaotic systems by hybrid biogeography-based optimization. Nonlinear Dynamics, 77(3), 983-992.
  • [33] Bayrak A. and Tatlicioglu E. 2013. Online time delay identification and control for general classes of nonlinear systems. Tr. of the Institute of Measurement and Control, 35(6), 808-823.
  • [34] Bayrak A. 2013. Online time delay identification and adaptive control for general classes of nonlinear systems. Izmir Institute of Technology, PhD dissertation, 165, Izmir, Turkey.
  • [35] Annaswamy A. M., Skantze F. P. and Loh A.-P. 1998. Adaptive control of continuous time systems with convex/concave parametrization. Automatica, 34(1), 33-49.
  • [36] Marquez H. J., Nonlinear Control Systems: Analysis and Design 1 st ed., John Wiley & Sons, New Jersey, (2003).
  • [37] Khalil H.K., Nonlinear Systems 3rEd., Prentice Hall, New Jersey, (2002).

Online Time Delay Estimation in Delay Differential Equation Based Chaotic Systems

Yıl 2017, Cilt: 3 Sayı: 3, 65 - 73, 27.12.2017

Öz

In this work, time delay estimation in delay differential equation based chaotic systems is handled. The time delay is handled as a parameter which effects the system nonlinearly. Under the light of this consideration, a nonlinear parameter estimator is utilized. The aforementioned method is based on Lyapunov stability analysis and assures global boundedness of all the signals and the convergence of the estimation error to the vicinity of zero. Several simulations are given to demonstrate the efficiency of the proposed time delay estimator for various delay differential equation based chaotic systems. From the numerical simulation studies, it is observed that the method works efficiently.

Kaynakça

  • [1] Pecora L. and Carroll T. 1990. Synchronization in chaotic systems. Physical Review Letters, 64, 821- 823.
  • [2] Pecora L. and Carroll T. 1991. Driving systems with chaotic signals. Physical Review Letters, 44, 2374-2383.
  • [3] Kocarev L., Hall K. S., Eckert K., Chua L. O., and Parlitz U. 1992. Experimental demonstration of secure communications via chaotic synchronization. Int. J. of Bifurcation and Chaos, 2(3), 709-713.
  • [4] Cuomo K. M. and Oppenheim A. V. 1993. Circuit implementation of synchronized chaos with applications to communication. Physical Review Letters, 71, 65-68.
  • [5] Richard J.-P. 2003. Time-delay systems: an overview of some recent advances and open problems. Automatica, 39(10), 1667-1694.
  • [6] Banerjee S. 2009. Synchronization of timedelayed systems with chaotic modulation and cryptography. Chaos, Solitons & Fractals, 42(2), 745-750.
  • [7] Udaltsov V. S., Goedgebuer J.-P., Larger L., Cuenot J.-B., Levy P., and Rhodes W. T. 2003. Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations. Physics Letters A, 308(1), 54-60.
  • [8] Udaltsov V. S., Larger L., Goedgebuer J. P., Locquet A. and Citrin D. S. 2005. Time delay identification in chaotic cryptosystems ruled by delay-differential equations. J. of Optical Technology, 72, 373-377.
  • [9] Tang Y., Cui M., Li L., Peng H. and Guan X. 2009. Parameter identification of time-delay chaotic system using chaotic ant swarm. Chaos, Solitons & Fractals, 41(4), 2097-2102.
  • [10] Banerjee S., Ghosh D., Ray A. and Chowdhury R. 2008. Synchronization between two different time-delayed systems and image encryption. A letter Journal Exploring the frontiers physics, 81(2), 1-6.
  • [11] Yalcin M. E. and Ozoguz S. 2007. n-scroll chaotic attractors from a first-order time-delay differential equation. American Institute of Physics, 17(033112), 1-8.
  • [12] Uçar A. and Bishop S.R. 2001. Chaotic behaviour in a nonlinear delay system. Int. J. of Nonlinear Sciences and Numerical Simulation, 2(3), 289-294.
  • [13] Ucar A. 2002. A prototype model for chaos studies. Int. J. Eng. Sci., 40(5), 251-258.
  • [14] Ucar A. 2003. On the chaotic behaviour of prototype delayed dynamical system. Chaos, Solitons & Fractals, 16(2), 187-194.
  • [15] Lu H. and He Z. 1996. Chaotic behavior in firstorder autonomous continuous-time systems with delay. IEEE Tr. on Circuits and Systems-I: Fundamental Theory and Applications, 43(8), 700- 702.
  • [16] Wang L. and Yang X. 2006. Generation of multi–scroll delayed chaotic oscillator. Electronics Letters, 42(25), 1439-1441.
  • [17] Mackey M. C. and Glass L. 1977. Oscillation and chaos in physiological control systems. Science, 197(4300), 287-289.
  • [18] Glass L., Beuter A. and Larocque D. 1988. Time delays, oscillations, and chaos in physiological control systems. Mathematical Biosciences, 90, 111- 125.
  • [19] Namajunas A., Pyragas K. and Tamasevicius A. 1995. An electronic analog of the Mackey–Glass system. Physics Letters A, 201, 42-46.
  • [20] Glass L. 2001. Synchronization and rhythmic processes in physiology. Nature, 410, 277-284.
  • [21] Tian Y.-C. and Gao F. 1998. Adaptive control of chaotic continuous-time systems with delay. Physica D, 117, 1-12.
  • [22] Wang H., Wang X., Zhu X.-J., Wang X.-H. 2012. Linear feedback controller design method for time-delay chaotic systems. Nonlinear Dynamics, 70(1), 355–362.
  • [23] Ponomarenko V. I. and Prokhorov M. D. 2002. Extracting information masked by the chaotic signal of a time-delay system. Physical Review E, 66, 1-7.
  • [24] Zhou C. and Lai C. H. 1999. Extracting messages masked by chaotic signals of time-delay systems. Physical Review E, 60, 1-4.
  • [25] Prokhorov M. D., Ponomarenko V. I., Karavaev A. S. and Bezruchko B. P. 2005. Reconstruction of time-delayed feedback systems from time series. Physica D: Nonlinear Phenomena, 203(3-4), 209- 223.
  • [26] Banerjee T., Biswas D. and Sarkar B. 2013. Anticipatory, complete and lag synchronization of chaos and hyperchaos in a nonlinear delay-coupled time-delayed system. Nonlinear Dynamics, 72(1-2), 321-332.
  • [27] Chen D., Zhang R., Ma X. and Liu S. 2012. Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme. Nonlinear Dynamics, 69(1-2), 35-55.
  • [28] Mensour B. and Longtin A. 1998. Synchronization of delay-differential equations with application to private communication. Physics Letters A, 244, 59-70.
  • [29] Beheshti S. and Khaloozadeh H. 2013. Synchronization of chaotic systems with unknown time delay by sliding mode observer approach and unknown delay identification. in Iranian Conf. on Electrical Eng., 14-16 May. Mashhad, Iran, 1-6.
  • [30] Ambika G. and Amritkar R. E. 2011. Delay or anticipatory synchronization in one-way coupled systems using variable delay with reset. Pramana - J. of Physics, 77(5), 891-904.
  • [31] Tang Y. and Guan X. 2009. Parameter estimation of chaotic system with time-delay: A differential evolution approach. Chaos, Solitons & Fractals, 42(5), 3132-3139.
  • [32] Lin J. 2014. Parameter estimation for time-delay chaotic systems by hybrid biogeography-based optimization. Nonlinear Dynamics, 77(3), 983-992.
  • [33] Bayrak A. and Tatlicioglu E. 2013. Online time delay identification and control for general classes of nonlinear systems. Tr. of the Institute of Measurement and Control, 35(6), 808-823.
  • [34] Bayrak A. 2013. Online time delay identification and adaptive control for general classes of nonlinear systems. Izmir Institute of Technology, PhD dissertation, 165, Izmir, Turkey.
  • [35] Annaswamy A. M., Skantze F. P. and Loh A.-P. 1998. Adaptive control of continuous time systems with convex/concave parametrization. Automatica, 34(1), 33-49.
  • [36] Marquez H. J., Nonlinear Control Systems: Analysis and Design 1 st ed., John Wiley & Sons, New Jersey, (2003).
  • [37] Khalil H.K., Nonlinear Systems 3rEd., Prentice Hall, New Jersey, (2002).
Toplam 37 adet kaynakça vardır.

Ayrıntılar

Bölüm Araştırma Makalesi
Yazarlar

Alper Bayrak Bu kişi benim

Enver Tatlıcıoğlu Bu kişi benim

Yayımlanma Tarihi 27 Aralık 2017
Gönderilme Tarihi 20 Ağustos 2017
Kabul Tarihi 12 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 3 Sayı: 3

Kaynak Göster

IEEE A. Bayrak ve E. Tatlıcıoğlu, “Zaman Gecikmeli Diferansiyel Denklem Tabanlı Kaotik Sistemlerde Çevrimiçi Zaman Gecikmesi Kestirimi”, GMBD, c. 3, sy. 3, ss. 65–73, 2017.

Gazi Journal of Engineering Sciences (GJES) publishes open access articles under a Creative Commons Attribution 4.0 International License (CC BY) 1366_2000-copia-2.jpg