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A general unified approach to chaos synchronization in continuous-time systems (with or without equilibrium points) as well as in discrete-time systems

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
By analyzing the issue of chaos synchronization, it can be noticed the lack of a general approach, which would enable any type of synchronization to be achieved. Similarly, there is the lack of a unified method for synchronizing both continuous-time and discrete-time systems via a scalar signal. This paper aims to bridge all these gaps by presenting a novel general unified framework to synchronize chaotic (hyperchaotic) systems via a scalar signal. By exploiting nonlinear observer design, the approach enables any type of synchronization defined to date to be achieved for both continuous-time and discrete-time systems. Referring to discrete-time systems, the method assures any type of dead beat synchronization (i.e., exact synchronization in finite time), thus providing additional value to the conceived framework. Finally, the topic of synchronizing special type of systems, such as those characterized by the absence of equilibrium points, is also discussed.
Rocznik
Strony
135--154
Opis fizyczny
Bibliogr. 26 poz., rys., tab., wykr., wzory
Twórcy
autor
  • Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy
autor
  • Department of Mathematics and Computer Science, University of Tebessa, 12002 Algeria
autor
  • School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Viet Nam
Bibliografia
  • [1] S. Rasappan and S. Vaidyanathan: Hybrid synchronization of n-scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback. Archives of Control Sciences, 22(3), (2012), 343-365.
  • [2] T. L. Carrol and L. M. Pecora: Synchronizing chaotic circuits. IEEE Transactions on Circuits and Systems, 38, (1991), 453-456.
  • [3] G. Wen, G. Grassi, Z. Feng and X. Liu: Special Issue on Advances in Nonlinear Dynamics and Control. Journal of the Franklin Institute, 8(352), (2015), 2985-2986.
  • [4] G. Grassi and S. Mascolo: Synchronization of high-order oscillators by observer design with application to hyperchaos-based cryptography. International Journal of Circuit Theory and Applications, 27 (1999), 543–553.
  • [5] G. Grassi and S. Mascolo: Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal. IEEE Transactions on Circuits and Systems - I, 44(10), (1997), 1011-1014.
  • [6] S. Vaidyanathan, C. Volos, V. T. Pham and K. Madhavanf: Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation. Archives of Control Sciences, 25(1), (2015), 135–158.
  • [7] G. Grassi: Observer-based hyperchaos synchronization in cascaded discrete-time systems. Chaos, Solitons & Fractals, 40(2), (2009), 1029–1039.
  • [8] D. A . Miller and G. Grassi: Experimental realization of observer-based hyperchaos synchronization. IEEE Transactions on Circuits and Systems - I, 48(3), (2001), 366-374.
  • [9] S. Vaidyanathan: Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system via backstepping control method. Archives of Control Sciences, 26(3), (2016), 311-338.
  • [10] S. Vaidyanathan and C. Volos: Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system. Archives of Control Sciences, 25(3), (2015), 333-353.
  • [11] R. Mainieri and J. Rehacek: Projective synchronization in threedimensional chaotic systems. Physical Review Letters, 82(15), (1999), 3042-3045.
  • [12] K. S. Ojo, A. N. Njah, S. T. Ogunjo and O. I. Olusola: Reduced order hybrid function projective combination synchronization of three Josephson junctions. Archives of Control Sciences, 24(1), (2014), 99-113.
  • [13] G. Grassi and D. A. Miller: Projective synchronization via a linear observer: application to time-delay, continuous-time and discrete-time systems. Int. Journal Bifurcation Chaos, 17(4), (2007), 1337-1344.
  • [14] M. Hu, Z. Xu, R. Zhang and A. Hu: Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyperchaotic) systems. Physics Letters A, 361 (2007), 231-237.
  • [15] M. Hu, Z. Xu and R. Zhanfg: Full state hybrid projective synchronization in continuous-time chaotic (hyperchaotic) systems. Communications in Nonlinear Science and Numerical Simulations, 13(2), (2008), 456-464.
  • [16] M. Hu, Z. Xu and R. Zhang: Full state hybrid projective synchronization of a general class of chaotic maps. Communications in Nonlinear Science and Numerical Simulations, 13(4), (2008), 782-789.
  • [17] L. Ren, R. Guo and U. E. Vincent: Coexistence of synchronization and anti-synchronization in chaotic systems. Archives of Control Sciences, 26(1), (2016), 69-79.
  • [18] G. Grassi: Propagation of projective synchronization in a series connection of chaotic systems. Journal of the Franklin Institute, 347(2), (2010), 438-451.
  • [19] V. T. Pham, A. Akgul, C. Volos, S. Jafari and T. Kapitaniak: Dynamics and circuit realization of a no-equilibrium chaotic system with a boostable variable. AEU – Int. Journal of Electronics and Communications, 78, (2017), 134-140.
  • [20] C. Li and J. C. Sprott: Variable-boostable chaotic flows. Optik, 127 (2016), 10389-10398.
  • [21] Y. D. Chu, Y. X. Chang, X. L. An, J. N. Yu and J. G. Zhang: A new scheme of general hybrid projective complete dislocated synchronization. Communications in Nonlinear Science and Numerical Simulations, 16(3), (2011), 1509-1516.
  • [22] G. Grassi: Continuous-time chaotic systems: Arbitrary full-state hybrid projective synchronization via a scalar signal. Chinese Physics B, 22(8), (2013), 080505.
  • [23] G. Grassi: Arbitrary full-state hybrid projective synchronization for chaotic discrete-time systems via a scalar signal. Chinese Physics B, 21(6), (2012), 060504.
  • [24] G. Grassi and D. A. Miller: Theory and experimental realization of observer-based discrete-time hyperchaos synchronization. IEEE Transactions on Circuits and Systems - I, 49(3), (2002), 373-378.
  • [25] E. Zeraoulia and J. C. Sprott: The discrete hyperchaotic double scroll. Int. Journal Bifurcation Chaos, 19(3), (2009), 1023–1027.
  • [26] R. C. Dorf and R. H. Bishop: Modern Control Systems. Prentice-Hall, Upper Saddle River, N. J. 2005.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-32e3bae5-bb56-43eb-b9aa-50987902b114
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