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Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

Autorzy
Vaidyanathan S.
Treść / Zawartość
Pełne teksty:
Vaidyanathan_analysis_ACS_3_2016.pdf
Identyfikatory
DOI
10.1515/acsc-2016-0018
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n ≥ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n ≥ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system with two nonlinearities has been proposed, and its qualitative properties have been detailed. The novel hyperjerk system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0.14219, L2 = 0.04605, L3 = 0 and L4 = −1.39267. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY = 3.1348. Next, an adaptive controller is designed via backstepping control method to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive controller is designed via backstepping control method to achieve global synchronization of the identical novel hyperjerk systems with three unknown parameters. MATLAB simulations are shown to illustrate all the main results derived in this research work on a novel hyperjerk system.
Słowa kluczowe
EN
Wydawca
Polish Academy of Sciences, Committee of Automatic Control and Robotics
Czasopismo
Archives of Control Sciences
Rocznik
2016
Tom
Vol. 26, no. 3
Strony
311--338
Opis fizyczny
Bibliogr. 90 poz., wykr., wzory
Twórcy
autor
Vaidyanathan S.
sundarvtu@gmail.com
  • Research and Development Centre, Vel Tech University, Avadi, Chennai-600062, Tamilnadu, India
Bibliografia
  • [1] A. T. Azar and S. Vaidyanathan: Chaos Modeling and Control Systems Design. Berlin, Springer, 2015.
  • [2] S. Vaidyanathan and C. Volos: Advances and Applications in Chaotic Systems. Berlin, Springer, 2016.
  • [3] E. N. Lorenz: Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20 (1963), 130–141.
  • [4] O. E. Rössler: An equation for continuous chaos. Physics Letters A, 57 (1976), 397–398.
  • [5] A. Arneodo, P. Coullet and C. Tresser: Possible new strange attractors with spiral structure. Communications in Mathematical Physics, 79 (1981), 573–579.
  • [6] J. C. Sprott: Some simple chaotic flows. Physical Review E, 50 (1994), 647–650.
  • [7] G. Chen and T. Ueta: Yet another chaotic attractor. International Journal of Bifurcation and Chaos, 9 (1999), 1465–1466.
  • [8] J. Lü and G. Chen: A new chaotic attractor coined. International Journal of Bifurcation and Chaos, 12 (2002), 659–661.
  • [9] C. X. iuU, T. Liu, L. Liu and K. Liu: A new chaotic attractor. Chaos, Solitons and Fractals, 22 (2004), 1031–1038.
  • [10] G. Cai and Z. Tan: Chaos synchronization of a new chaotic system via nonlinear control. Journal of Uncertain Systems, 1 (2007), 235-240.
  • [11] G. Tigan and D. Opris: Analysis of a 3D chaotic system. Chaos, Solitons and Fractals, 36 (2008), 1315–1319.
  • [12] D. Li: A three-scroll chaotic attractor. Physics Letters A, 372 (2008), 387–393.
  • [13] V. Sundarapandian and I. Pehlivan: Analysis, control, synchronization and circuit design of a novel chaotic system. Mathematical and Computer Modelling, 55 (2012), 1904–1915.
  • [14] V. Sundarapandian: Analysis and anti-synchronization of a novel chaotic system via active and adaptive controllers. Journal of Engineering Science and Technology Review, 6 (2013), 45–52.
  • [15] S. Vaidyanathan: A new six-term 3-D chaotic system with an exponential nonlinearity. Far East Journal of Mathematical Sciences, 79 (2013), 135–143.
  • [16] S. Vaidyanathan: Analysis and adaptive synchronization of two novel chaotic systems with hyperbolic sinusoidal and cosinusoidal nonlinearity and unknown parameters. Journal of Engineering Science and Technology Review, 6 (2013), 53–65.
  • [17] S. Vaidyanathan: A new eight-term 3-D polynomial chaotic system with three quadratic nonlinearities. Far East Journal of Mathematical Sciences, 84 (2014), 219–226.
  • [18] S. Vaidyanathan: Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities. International Journal of Modelling, Identification and Control, 22 (2014), 41–53.
  • [19] S. Vaidyanathan and K. Madhavan: Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system. International Journal of Control Theory and Applications, 6 (2013), 121–137.
  • [20] S. Vaidyanathan: Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities. European Physical Journal: Special Topics, 223 (2014), 1519–1529.
  • [21] S. Vaidyanathan, Ch. Volos, V. T. Pham, K. Madhavan and B. A. Idowu: Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities. Archives of Control Sciences, 24 (2014), 257–285.
  • [22] S. Vaidyanathan: Generalised projective synchronisation of novel 3-D chaotic systems with an exponential non-linearity via active and adaptive control. International Journal of Modelling, Identification and Control, 22 (2014), 207–217.
  • [23] 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), (2016), 333–353.
  • [24] S. Vaidyanathan: Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity. International Journal of Modelling, Identification and Control, 23 (2015), 164–172.
  • [25] S. Vaidyanathan: A 3-D novel highly chaotic system with four quadratic nonlinearities, its adaptive control and anti-synchronization with unknown parameters. Journal of Engineering Science and Technology Review, 8 (2015), 106–115.
  • [26] S. Vaidyanathan: Analysis, control and synchronization of a 3-D novel jerk chaotic system with two quadratic nonlinearities. Kyungpook Mathematical Journal, 55 (2015), 563–586.
  • [27] S. Vaidyanathan: A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control. Archives of Control Sciences, 26 (1), (2016), 19–47.
  • [28] S. Vaidyanathan and S. Pakiriswamy: A five-term 3-D novel conservative chaotic system and its generalized projective synchronization via adaptive control method. International Journal of Control Theory and Applications, 9 (1), (2016), 61–78.
  • [29] S. Vaidyanathan: A novel 3-D conservative chaotic system with a sinusoidal nonlinearity and its adaptive control. International Journal of Control Theory and Applications, 9 (1), (2016), 115–132.
  • [30] S. Vaidyanathan: Mathematical analysis, adaptive control and synchronization of a ten-term novel three-scroll chaotic system with four quadratic nonlinearities. International Journal of Control Theory and Applications, 9 (1), (2016), 1–20.
  • [31] S. Vaidyanathan and K. Rajagopal: Analysis, control, synchronization and LabVIEW implementation of a seven-term novel chaotic system. International Journal of Control Theory and Applications, 9 (1), (2016), 151–174.
  • [32] S. Vaidyanathan and S. Pakiriswamy: Adaptive control and synchronization design of a seven-term novel chaotic system with a quartic nonlinearity. International Journal of Control Theory and Applications, 9 (1), (2016), 237–256.
  • [33] S. Vaidyanathan: A highly chaotic system with four quadratic nonlinearities, its analysis, control and synchronization via integral sliding mode control. International Journal of Control Theory and Applications, 9 (1), (2016), 279–297.
  • [34] S. Vaidyanathan: A novel 3-D jerk chaotic system with two quadratic nonlinearities and its adaptive control. International Journal of Control Theory and Applications, 9 (1), (2016), 199–219.
  • [35] I. Pehlivan, I. M. Moroz and S. Vaidyanathan: Analysis, synchronization and circuit design of a novel butterfly attractor. Journal of Sound and Vibration, 333 (2014), 5077–5096.
  • [36] S. Jafari and J. C. Sprott: Simple chaotic flows with a line equilibrium. Chaos, Solitons and Fractals, 57 (2013), 79–84.
  • [37] V. T. Pham, C. Volos, S. Jafari, Z. Wei and X. Wang: Constructing a novel no-equilibrium chaotic system. International Journal of Bifurcation and Chaos, 24 (2014), 1450073.
  • [38] V. T. Pham, S. Jafari, S. Vaidyanathan, C. Volos and X. WANG: A novel memristive neural network with hidden attractors and its circuitry implementation. Science China Technological Sciences, 59 (2016), 358–363.
  • [39] V. T. Pham, C. Volos, S. Jafari, S. Vaidyanathan, T. Kapitaniak and X. Wang: A chaotic system with different families of hidden attractors. International Journal of Bifurcation and Chaos, 26 (2016),1650139.
  • [40] V. T. Pham, S. Vaidyanathan, C. K. Volos, S. Jafari, N. V. Kuznetsov and T. M. Hoang: A novel memristive time-delay chaotic system without equilibrium points. European Physical Journal: Special Topics, 225 (1), (2016), 127–136.
  • [41] S. Sampath, S. Vaidyanathan, C. K. Volos and V.-T. Pham: An eight-term novel four-scroll chaotic system with cubic nonlinearity and its circuit simulation. Journal of Engineering Science and Technology Review, 8 (2015), 1–6.
  • [42] A. Akgul, I. Moroz, I. Pehlivan and S. Vaidyanathan: A new four-scroll chaotic attractor and its engineering applications. Optik, 127 (2016), 5491–5499.
  • [43] J. C. Sprott: Elegant Chaos. Singapore, World Scientific, 2010.
  • [44] C. Li, X. Liao and K. W. Wong: Lag synchronization of hyperchaos with application to secure communications. Chaos, Solitons and Fractals, 23 (2005), 183–193.
  • [45] N. Smaoui, A. Karouma and M. Zribi: Secure communications based on the synchronization of the hyperchaotic Chen and the unified chaotic systems. Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 3279–3293.
  • [46] T. I. Chien and T. L. Liao: Design of secure digital communication systems using chaotic modulation, cryptography and chaotic synchronization. Chaos, Solitons & Fractals, 24 (2005), 241–245.
  • [47] B. Zhang, M. Chen and D. Zhou: Chaotic secure communication based on particle filtering. Chaos, Solitons & Fractals, 30 (2006), 1273–1280.
  • [48] Q. Zhang, L. Guo and X. Wei: A novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Optik, 124 (2013), 3596–3600.
  • [49] H. Liu, X. Wang and A. Kadir: Color image encryption using Choquet fuzzy integral and hyper chaotic system. Optik, 124 (2013), 3257–3533.
  • [50] A. Buscarino, L. Fortuna and M. Frasca: Experimental robust synchronization of hyperchaotic circuits. Physica D: Nonlinear Phenomena, 238 (2009), 1917–1922.
  • [51] N. Yujun, W. Xingyuan, W. Mingjun and Z. Huaguang: A new hyperchaotic system and its circuit implementation. Communications in Nonlinear Science and Numerical Simulation, 15 (2010), 3518–3524.
  • [52] O. E. Rössler: An equation for hyperchaos. Physics Letters A, 71 (1979), 155–157.
  • [53] Q. Jia: Hyperchaos generated from the Lorenz chaotic system and its control. Physics Letters A, 366 (2007), 217–222.
  • [54] A. Chen, J. Lu, J. Lü and S. Yu: Generating hyperchaotic Lü attractor via state feedback control. Physica A, 364 (2006), 103–110.
  • [55] X. Li: Modified projective synchronization of a new hyperchaotic system via nonlinear control. Communications in Theoretical Physics, 52 (2009), 274–278.
  • [56] J. Wang and Z. Chen: A novel hyperchaotic system and its complex dynamics. International Journal of Bifurcation and Chaos, 18 (2008), 3309–3324.
  • [57] D. Ghosh and S. Bhattacharya: Projective synchronization of new hyperchaotic system with fully unknown parameters. Nonlinear Dynamics, 61 (2010), 11–21.
  • [58] Q. Jia: Hyperchaos generated from the Lorenz chaotic system and its control. Physics Letters A, 366 (2007), 217–222.
  • [59] S. Vaidyanathan: A ten-term novel 4-D hyperchaotic system with three quadratic nonlinearities and its control. International Journal of Control Theory and Applications, 6 (2013), 97–109.
  • [60] S. Vaidyanathan, Ch. Volosa and V. T. Pham: Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation. Archives of Control Sciences, 24 (2014), 409–446.
  • [61] S. Vaidyanathan: Qualitative analysis and control of an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. International Journal of Control Theory and Applications, 7 (2014), 35–47.
  • [62] S. Vaidyanathan and A .T. Azar: Analysis and control of a 4-D novel hyperchaotic system. Studies in Computational Intelligence, 581 (2015), 3–17.
  • [63] S. Vaidyanathan, Ch. K. Volos and V. T. Pham: Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation. Archives of Control Sciences, 24 (4), (2014), 409–446.
  • [64] S. Vaidyanathan, C. Volos, V. T. Pham and K. Madhavan: 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.
  • [65] S. Vaidyanathan, C. K. Volos and V. T. Pham: Analysis, control, synchronization and SPICE implementation of a novel 4-D hyperchaotic Rikitake dynamo system without equilibrium. Journal of Engineering Science and Technology Review, 8 (2), (2015), 232–244.
  • [66] S. Vaidyanathan, V. T. Pham and C. K. Volos: A 5-D hyperchaotic Rikitake dynamo system with hidden attractors. European Physical Journal: Special Topics, 224 (2015), 1575–1592.
  • [67] S. Vaidyanathan and A. Boulkroune: A novel hyperchaotic system with two quadratic nonlinearities, its analysis and synchronization via integral sliding mode control. International Journal of Control Theory and Applications, 9 (1), (2016), 321–337.
  • [68] S. Vaidyanathan: An eleven-term novel 4-D hyperchaotic system with three quadratic nonlinearities, analysis, control and synchronization via adaptive control method. International Journal of Control Theory and Applications, 9 (1), (2016), 21–43.
  • [69] V. T. Pham, S. Vaidyanathan, C. Volos, S. Jafari and S.T. KINGNI: A no-equilibrium hyperchaotic system with a cubic nonlinear term. Optik, 127(6), (2016), 3259–3265.
  • [70] S. Sampath, S. Vaidyanathan and V. T. Pham: A novel 4-D hyperchaotic system with three quadratic nonlinearities, its adaptive control and circuit simulation. International Journal of Control Theory and Applications. 9 (1), (2016), 339–356.
  • [71] K. E. Chlouverakis and J. C. Sprott: Chaotic hyperjerk systems. Chaos, Solitons and Fractals, 28 (2006), 739–746.
  • [72] G. Cai and W. Tu: Adaptive backstepping control of the uncertain unified chaotic system. International Journal of Nonlinear Science, 4 (2007), 17–24.
  • [73] M. T. Yassen: Controlling, synchronization and tracking chaotic Liu system using active backstepping design. Physics Letters A, 360 (2007), 582–587.
  • [74] J. A. Laoye, U .E. Vincent and S. O. Kareem: Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller. Chaos, Solitons and Fractals, 39 (2009), 356–362.
  • [75] S. Vaidyanathan: Adaptive backstepping controller and synchronizer design for Arneodo chaotic system with unknown parameters. International Journal of Computer Science and Information Technology, 4 (2012), 145–159.
  • [76] S. Vaidyanathan and K. Rajagopal: Hybrid synchronization of hyperchaotic Wang-Chen and hyperchaotic lorenz systems by active non-linear control. International Journal of Signal System Control and Engineering Application, 4 (2011), 55–61.
  • [77] R. Karthikeyan and V. Sundarapandian: Hybrid chaos synchronization of four-scroll systems via active control. Journal of Electrical Engineering, 65 (2014), 97–103.
  • [78] V. Sundarapandian and R. Karthikeyan: Anti-synchronization of Lü and Pan chaotic systems by adaptive nonlinear control. European Journal of Scientific Research, 64 (2011), 94–106.
  • [79] V. Sundarapandian and R. Karthikeyan: Adaptive anti-synchronization of Uncertain Tigan and Li Systems. Journal of Engineering and Applied Sciences, 7 (2012), 45–52.
  • [80] X. Tan, J. Zhang and Y. Yang: Synchronizing chaotic systems using backstepping design. Chaos, Solitons and Fractals, 16 (2003), 37–45.
  • [81] S. Rasappan and S. Vaidyanathan: Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control. Far East Journal of Mathematical Sciences, 67 (2012), 265–287.
  • [82] S. Rasappan and S. Vaidyanathan: Synchronization of hyperchaotic Liu system via backstepping control with recursive feedback. Communications in Computer and Information Science, 305 (2012), 212–221.
  • [83] S. Rasappan and S. Vaidyanathan: Hybrid synchronization of n-scroll Chua circuits using adaptive backstepping control design with recursive feedback. Malaysian Journal of Mathematical Sciences, 7 (2013), 219–226.
  • [84] V. Sundarapandian and S. Sivaperumal: Sliding controller design of hybrid synchronization of four-wing chaotic systems. International Journal of Soft Computing, 6 (2011), 224–231.
  • [85] S. Vaidyanathan: Global chaos control of hyperchaotic Liu system via sliding control method. International Journal of Control Theory and Applications, 5 (2012), 117–123.
  • [86] S. Vaidyanathan and S. Sampath: Anti-synchronization of four-wing chaotic systems via sliding mode control. International Journal of Automatic Computing, 9 (2012), 274–279.
  • [87] S. Vaidyanathan: Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control. International Journal of Modelling, Identification and Control, 22 (2014), 170–177.
  • [88] S. Vaidyanathan and S. Sampath: Anti-synchronization of identical chaotic systems via novel sliding control method with application to Vaidyanathan-Madhavan chaotic system. International Journal of Control Theory and Applications, 9 (1), (2016), 85–100.
  • [89] S. Sampath and S. Vaidyanathan: Hybrid synchronization of identical chaotic systems via novel sliding control method with application to Sampath four-scroll chaotic system. International Journal of Control Theory and Applications, 9 (1), (2016), 221–235.
  • [90] H. K. Khalil: Nonlinear Systems, Prentice Hall, New Jersey, 2002.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c9f84c0b-2b84-45ca-b45a-611a96f220da
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