Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Adaptive Sliding Mode Control of the Furuta Pendulum Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Hybrid Synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan Chaotic Systems

verfasst von : Sundarapandian Vaidyanathan, Ahmad Taher Azar

Erschienen in: Advances and Applications in Sliding Mode Control systems

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Hybrid phase synchronization is a new type of synchronization of a pair of chaotic systems called the master and slave systems. In hybrid phase synchronization, the odd numbered states of the master and slave systems are completely synchronized (CS), while their even numbered states are anti-synchronized (AS). The hybrid phase synchronization has applications in secure communications and cryptosystems. This work derives a new result for the hybrid phase synchronization of identical chaotic systems using sliding mode control. The main result has been proved using Lyapunov stability theory. Sliding mode control (SMC) is well-known as a robust approach and useful for controller design in systems with parameter uncertainties. As an application of this general result, a sliding mode controller is derived for the hybrid phase synchronization of the identical 3-D Vaidyanathan chaotic systems (2014). MATLAB simulations have been provided to illustrate the Vaidyanathan system and the hybrid synchronizer results for the identical Vaidyanathan systems.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Anti-synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan–Madhavan Chaotic Systems
Nächstes Kapitel Global Chaos Control of a Novel Nine-Term Chaotic System via Sliding Mode Control
Literatur
Arneodo, A., Coullet, P., Tresser, C.: Possible new strange attractors with spiral structure. Common. Math. Phys. 79(4), 573–576 (1981)CrossRefMathSciNetMATH
Bidarvatan, M., Shahbakhti, M., Jazayeri, S.A., Koch, C.R.: Cycle-to-cycle modeling and sliding mode control of blended-fuel HCCI engine. Control Eng. Pr 24, 79–91 (2014)
Cai, G., Tan, Z.: Chaos synchronization of a new chaotic system via nonlinear control. J. Uncertain Syst. 1(3), 235–240 (2007)
Carroll, T.L., Pecora, L.M.: Synchronizing chaotic circuits. IEEE Trans. Circuits Syst. 38(4), 453–456 (1991)CrossRef
Chen, W.-H., Wei, D., Lu, X.: Global exponential synchronization of nonlinear time-delay Lure systems via delayed impulsive control. Commun. Nonlinear Sci. Numer. Simul. 19(9), 3298–3312 (2014)CrossRefMathSciNet
Das, S., Goswami, D., Chatterjee, S., Mukherjee, S.: Stability and chaos analysis of a novel swarm dynamics with applications to multi-agent systems. Eng. Appl. Artif. Intell. 30, 189–198 (2014)CrossRef
Feki, M.: An adaptive chaos synchronization scheme applied to secure communication. Chaos, Solitons Fractals 18(1), 141–148 (2003)CrossRefMathSciNetMATH
Gan, Q., Liang, Y.: Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control. J. Frankl. Inst. 349(6), 1955–1971 (2012)CrossRefMathSciNet
Gaspard, P.: Microscopic chaos and chemical reactions. Physica A: Stat. Mech. Appl 263(1–4), 315–328 (1999)CrossRef
Gibson, W.T., Wilson, W.G.: Individual-based chaos: Extensions of the discrete logistic model. J. Theor. Biol. 339, 84–92 (2013)
Guégan, D.: Chaos in economics and finance. Ann. Rev. Control 33(1), 89–93 (2009)CrossRef
Hamayun, M.T., Edwards, C., Alwi, H.: A fault tolerant control allocation scheme with output integral sliding modes. Automatica 49(6), 1830–1837 (2013)CrossRefMathSciNet
Huang, J.: Adaptive synchronization between different hyperchaotic systems with fully uncertain parameters. Phys. Lett. A 372(27–28), 4799–4804 (2008)CrossRefMATH
Huang, X., Zhao, Z., Wang, Z., Li, Y.: Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing 94, 13–21 (2012)CrossRef
Jiang, G.-P., Zheng, W.X., Chen, G.: Global chaos synchronization with channel time-delay. Chaos, Solitons Fractals 20(2), 267–275 (2004)CrossRefMathSciNetMATH
Karthikeyan, R., Sundarapandian, V.: Hybrid chaos synchronization of four-scroll systems via active control. J. Elect. Eng. 65(2), 97–103 (2014)
Kaslik, E., Sivasundaram, S.: Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32, 245–256 (2012)CrossRefMATH
Kengne, J., Chedjou, J.C., Kenne, G., Kyamakya, K.: Dynamical properties and chaos synchronization of improved Colpitts oscillators. Commun. Nonlinear Sci. Numer Simul. 17(7), 2914–2923 (2012)CrossRefMathSciNet
Khalil, H.K.: Nonlinear Systems. Prentice Hall, Upper Saddle River (2001)
Kyriazis, M.: Applications of chaos theory to the molecular biology of aging. Exp. Gerontol. 26(6), 569–572 (1991)CrossRef
Li, N., Pan, W., Yan, L., Luo, B., Zou, X.: Enhanced chaos synchronization and communication in cascade-coupled semiconductor ring lasers. Commun. Nonlinear Sci. Numer. Simul. 19(6), 1874–1883 (2014)CrossRef
Li, N., Zhang, Y., Nie, Z.: Synchronization for general complex dynamical networks with sampled-data. Neurocomputing 74(5), 805–811 (2011)CrossRef
Lian, S., Chen, X.: Traceable content protection based on chaos and neural networks. Appl. Soft Comput. 11(7), 4293–4301 (2011)CrossRef
Lin, W.: Adaptive chaos control and synchronization in only locally Lipschitz systems. Phys. Lett. A 372(18), 3195–3200 (2008)CrossRefMathSciNetMATH
Liu, C., Liu, T., Liu, L., Liu, K.: A new chaotic attractor. Chaos, Solitions Fractals 22(5), 1031–1038 (2004)CrossRefMATH
Liu, L., Zhang, C., Guo, Z.A.: Synchronization between two different chaotic systems with nonlinear feedback control. Chin. Phys. 16(6), 1603–1607 (2007)CrossRef
Lorenz, E.N.: Deterministic periodic flow. J. Atmos. Sci. 20(2), 130–141 (1963)CrossRef
Lü, J., Chen, G.: A new chaotic attractor coined. Intern. J. Bifurc. Chaos 12(3), 659–661 (2002)CrossRefMATH
Lu, W., Li, C., Xu, C.: Sliding mode control of a shunt hybrid active power filter based on the inverse system method. Intern. J. Elect. Power Energy Syst. 57, 39–48 (2014)CrossRef
Mondal, S., Mahanta, C.: Adaptive second order terminal sliding mode controller for robotic manipulators. J. Franklin Inst. 351(4), 2356–2377 (2014)CrossRefMathSciNet
Murali, K., Lakshmanan, M.: Secure communication using a compound signal from generalized chaotic systems. Phys. Lett. A 241(6), 303–310 (1998)CrossRefMATH
Nehmzow, U., Walker, K.: Quantitative description of robotenvironment interaction using chaos theory. Robot. Auton. Syst. 53(3–4), 177–193 (2005)CrossRef
Njah, A.N., Ojo, K.S., Adebayo, G.A., Obawole, A.O.: Generalized control and synchronization of chaos in RCL-shunted Josephson junction using backstepping design. Physica C 470(13–14), 558–564 (2010)CrossRef
Ouyang, P.R., Acob, J., Pano, V.: PD with sliding mode control for trajectory tracking of robotic system. Robot. Comput. Integr. Manuf. 30(2), 189–200 (2014)CrossRef
Perruquetti, W., Barbot, J.P.: Sliding Mode Control in Engineering. Marcel Dekker, New York (2002)
Petrov, V., Gaspar, V., Masere, J., Showalter, K.: Controlling chaos in Belousov-Zhabotinsky reaction. Nature 361, 240–243 (1993)CrossRef
Qu, Z.: Chaos in the genesis and maintenance of cardiac arrhythmias. Prog. Biophys. Mol. Biol. 105(3), 247–257 (2011)CrossRef
Rafikov, M., Balthazar, J.M.: On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Commun. Nonlinear Sci. Numer. Simul. 13(7), 1246–1255 (2007)CrossRefMathSciNet
Rasappan, S., Vaidyanathan, S.: Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control. Far East J. Math. Sci. 67(2), 265–287 (2012a)MathSciNetMATH
Rasappan, S., Vaidyanathan, S.: Hybrid synchronization of n-scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback. Arch. Control Sci. 22(3), 343–365 (2012b)MATH
Rhouma, R., Belghith, S.: Cryptoanalysis of a chaos based cryptosystem on DSP. Commun. Nonlinear Sci. Numer. Simul. 16(2), 876–884 (2011)CrossRefMathSciNetMATH
Rössler, O.E.: An equation for continuous chaos. Phys. Lett. 57A(5), 397–398 (1976)CrossRef
Sarasu, P., Sundarapandian, V.: Adaptive controller design for the generalized projective synchronization of 4-scroll systems. Intern. J. Syst. Signal Control Eng. Appl. 5(2), 21–30 (2012a)
Sarasu, P., Sundarapandian, V.: Generalized projective synchronization of two-scroll systems via adaptive control. Int. J. Soft Comput. 7(4), 146–156 (2012b)CrossRef
Sarasu, P., Sundarapandian, V.: Generalized projective synchronization of two-scroll systems via adaptive control. Eur. J. Sci. Res. 72(4), 504–522 (2012c)
Shahverdiev, E.M., Bayramov, P.A., Shore, K.A.: Cascaded and adaptive chaos synchronization in multiple time-delay laser systems. Chaos, Solitons Fractals 42(1), 180–186 (2009)CrossRef
Shahverdiev, E.M., Shore, K.A.: Impact of modulated multiple optical feedback time delays on laser diode chaos synchronization. Optics Commun. 282(17), 3568–3572 (2009)CrossRef
Sharma, A., Patidar, V., Purohit, G., Sud, K.K.: Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping. Commun. Nonlinear Sci. Numer. Simul. 17(6), 2254–2269 (2012)CrossRefMathSciNet
Suérez, I.: Mastering chaos in ecology. Ecol. Model. 117(2–3), 305–314 (1999)CrossRef
Sundarapandian, V.: Output regulation of the Lorenz attractor. Far East J. Math. Sci. 42(2), 289–299 (2010)MathSciNetMATH
Sundarapandian, V., Karthikeyan, R.: Hybrid synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems via active control. J. Eng. Appl. Sci. 7(3), 254–264 (2012)CrossRef
Sundarapandian, V., Pehlivan, I.: Analysis, control, synchronization, and circuit design of a novel chaotic system. Math. Comput. Model. 55(7–8), 1904–1915 (2012)CrossRefMathSciNetMATH
Suresh, R., Sundarapandian, V.: Global chaos synchronizatoin of a family of \(n\)-scroll hyperchaotic Chua circuits using backstepping control with recursive feedback. Far East J. Math. Sci. 73(1), 73–95 (2013)MATH
Tu, J., He, H., Xiong, P.: Adaptive backstepping synchronization between chaotic systems with unknown Lipschitz constant. Appl. Math. Comput. 236, 10–18 (2014)CrossRefMathSciNet
Ucar, A., Lonngren, K.E., Bai, E.W.: Chaos synchronization in RCL-shunted Josephson junction via active control. Chaos, Solitons Fractals 31(1), 105–111 (2007)CrossRef
Usama, M., Khan, M.K., Alghatbar, K., Lee, C.: Chaos-based secure satellite imagery cryptosystem. Comput. Math. Appl. 60(2), 326–337 (2010)CrossRefMathSciNetMATH
Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, New York (1992)
Vaidyanathan, S.: Anti-synchronization of Newton-Leipnik and Chen-Lee chaotic systems by active control. Intern. J. Control Theory Appl. 4(2), 131–141 (2011)
Vaidyanathan, S.: Adaptive backstepping controller and synchronizer design for Arneodo chaotic system with unknown parameters. Intern. J. Comput. Sci. Inform. Technol. 4(6), 145–159 (2012a)CrossRef
Vaidyanathan, S.: Anti-synchronization of Sprott-L and Sprott-M chaotic systems via adaptive control. Intern. J. Control Theory Appl. 5(1), 41–59 (2012b)MathSciNet
Vaidyanathan, S.: Output regulation of the Liu chaotic system. Appl. Mech. Mater. 110–116, 3982–3989 (2012c)
Vaidyanathan, S.: A new six-term 3-D chaotic system with an exponential nonlinearity. Far East J. Math. Sci. 79(1), 135–143 (2013a)MATH
Vaidyanathan, S.: Analysis and adaptive synchronization of two novel chaotic systems with hyperbolic sinusoidal and cosinusoidal nonlinearity and unknown parameters. J. Eng. Sci. Technol. Rev. 6(4), 53–65 (2013b)MathSciNet
Vaidyanathan, S.: A new eight-term 3-D polynomial chaotic system with three quadratic nonlinearities. Far East J. Math. Sci. 84(2), 219–226 (2014)MathSciNetMATH
Vaidyanathan, S., Rajagopal, K.: Global chaos synchronization of four-scroll chaotic systems by active nonlinear control. Intern. J. Control Theory Appl. 4(1), 73–83 (2011a)
Vaidyanathan, S., Rajagopal, K.: Hybrid synchronization of hyperchaotic Wang-Chen and hyperchaotic Lorenz systems by active nonlinear control. Intern. J. Syst. Signal Control Eng. Appl. 4(3), 55–61 (2011b)
Vaidyanathan, S., Sampath, S.: Anti-synchronization of four-scroll chaotic systems via sliding mode control. Int. J. Autom. Comput. 9(3), 274–279 (2012)CrossRef
Volos, C.K., Kyprianidis, I.M., Stouboulos, I.N.: Experimental investigation on coverage performance of a chaotic autonomous mobile robot. Robot. Autonom. Syst. 61(12), 1314–1322 (2013)CrossRef
Wang, F., Liu, C.: A new criterion for chaos and hyperchaos synchronization using linear feedback control. Phys. Lett. A 360(2), 274–278 (2006)CrossRefMATH
Wu, X., Guan, Z.-H., Wu, Z.: Adaptive synchronization between two different hyperchaotic systems. Nonlinear Analysis: Theory, Methods Appl. 68(5), 1346–1351 (2008)CrossRefMathSciNetMATH
Xiao, X., Zhou, L., Zhang, Z.: Synchronization of chaotic Lure systems with quantized sampled-data controller. Commun. Nonlinear Sci. Numer. Simul. 19(6), 2039–2047 (2014)CrossRefMathSciNet
Yuan, G., Zhang, X., Wang, Z.: Generation and synchronization of feedback-induced chaos in semiconductor ring lasers by injection-locking. Optik Intern. J. Light Electron Optics 125(8), 1950–1953 (2014)CrossRef
Zaher, A.A., Abu-Rezq, A.: On the design of chaos-based secure communication systems. Commun. Nonlinear Syst. Numer. Simul. 16(9), 3721–3727 (2011)CrossRefMathSciNetMATH
Zhang, H., Zhou, J.: Synchronization of sampled-data coupled harmonic oscillators with control inputs missing. Syst. Control Lett. 61(12), 1277–1285 (2012)CrossRefMATH
Zhang, J., Li, C., Zhang, H., Yu, J.: Chaos synchronization using single variable feedback based on backstepping method. Chaos, Solitons Fractals 21(5), 1183–1193 (2004)CrossRefMathSciNetMATH
Zhang, X., Liu, X., Zhu, Q.: Adaptive chatter free sliding mode control for a class of uncertain chaotic systems. Appl. Math. Comput. 232, 431–435 (2014)CrossRefMathSciNet
Zhou, W., Xu, Y., Lu, H., Pan, L.: On dynamics analysis of a new chaotic attractor. Phys. Lett. A 372(36), 5773–5777 (2008)CrossRefMathSciNetMATH
Metadaten
Titel
Hybrid Synchronization of Identical Chaotic Systems Using Sliding Mode Control and an Application to Vaidyanathan Chaotic Systems
verfasst von
Sundarapandian Vaidyanathan
Ahmad Taher Azar
Copyright-Jahr
2015
Buch
Advances and Applications in Sliding Mode Control systems

Print ISBN: 978-3-319-11172-8

Electronic ISBN: 978-3-319-11173-5

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-11173-5_20