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Adaptive Control and Synchronization of a Rod-Type Plasma Torch Chaotic System via Backstepping Control Method

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Advances and Applications in Chaotic Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 636))

Abstract

In this work, we first describe the Ghorui jerk chaotic system (2000) describing a strange attractor of a thermal arc plasma system based on triple convection theory. The phase portraits of the rod-type plasma torch chaotic system are displayed and the dynamic properties of the rod-type plasma torch chaotic system are discussed. We show that the rod-type plasma torch chaotic system has three unstable equilibrium points on the \(x_1\)-axis. The Lyapunov exponents of the rod-type plasma torch chaotic system are obtained as \(L_1 = 0.3451\), \(L_2 = 0\) and \(L_3 = -1.3509\). Clearly, the Maximal Lyapunov Exponent (MLE) of the rod-type plasma torch chaotic system is given by \(L_1 = 0.3451\). Since the sum of the Lyapunov exponents of the rod-type plasma torch chaotic system is negative, the chaotic system is dissipative. Also, the Kaplan–Yorke dimension of the rod-type plasma torch chaotic system is obtained as \(D_{KY} = 2.2555\). Next, an adaptive backstepping controller is designed to globally stabilize the rod-type plasma torch chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical rod-type plasma torch chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations have been shown to illustrate all the main results derived in this work.

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References

  1. Abdurrahman A, Jiang H, Teng Z (2015) Finite-time synchronization for memristor-based neural networks with time-varying delays. Neural Netw 69:20–28

    Article  Google Scholar 

  2. Arneodo A, Coullet P, Tresser C (1981) Possible new strange attractors with spiral structure. Commun Math Phys 79(4):573–576

    Article  MathSciNet  MATH  Google Scholar 

  3. Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design, vol 581. Springer, Germany

    Google Scholar 

  4. Behnia S, Afrang S, Akhshani A, Mabhouti K (2013) A novel method for controlling chaos in external cavity semiconductor laser. Optik 124(8):757–764

    Article  Google Scholar 

  5. Cai G, Tan Z (2007) Chaos synchronization of a new chaotic system via nonlinear control. J Uncertain Syst 1(3):235–240

    Google Scholar 

  6. Carroll TL, Pecora LM (1991) Synchronizing chaotic circuits. IEEE Trans Circuits Syst 38(4):453–456

    Article  MATH  Google Scholar 

  7. Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9(7):1465–1466

    Article  MathSciNet  MATH  Google Scholar 

  8. Chen WH, Wei D, Lu X (2014) Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control. Commun Nonlinear Sci Numer Simul 19(9):3298–3312

    Article  MathSciNet  Google Scholar 

  9. Gan Q, Liang Y (2012) 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

    Article  MathSciNet  MATH  Google Scholar 

  10. Ghorui S, Sahasrabudhe SN, Muryt PSS, Das AK, Venkatramani N (2000) Experimental evidence of chaotic behavior in atmosphere pressure arc discharge. IEEE Trans Plasma Sci 28(1):253–260

    Article  Google Scholar 

  11. Islam MM, Murase K (2005) Chaotic dynamics of a behaviour-based miniature mobile robot: effects of environment and control structure. Neural Netw 18(2):123–144

    Article  Google Scholar 

  12. Jiang GP, Zheng WX, Chen G (2004) Global chaos synchronization with channel time-delay. Chaos Solitons Fractals 20(2):267–275

    Article  MathSciNet  MATH  Google Scholar 

  13. Karthikeyan R, Sundarapandian V (2014) Hybrid chaos synchronization of four-scroll systems via active control. J Electr Eng 65(2):97–103

    Google Scholar 

  14. Khalil HK (2001) Nonlinear systems, 3rd edn. Prentice Hall, New Jersey

    Google Scholar 

  15. Li D (2008) A three-scroll chaotic attractor. Phys Lett A 372(4):387–393

    Article  MathSciNet  MATH  Google Scholar 

  16. Li GH, Zhou SP, Yang K (2007) Controlling chaos in Colpitts oscillator. Chaos Solitons Fractals 33:582–587

    Article  Google Scholar 

  17. Li N, Zhang Y, Nie Z (2011) Synchronization for general complex dynamical networks with sampled-data. Neurocomputing 74(5):805–811

    Article  Google Scholar 

  18. Lorenz EN (1963) Deterministic periodic flow. J Atmos Sci 20(2):130–141

    Article  Google Scholar 

  19. Lü J, Chen G (2002) A new chaotic attractor coined. Int J Bifurc Chaos 12(3):659–661

    Article  MathSciNet  MATH  Google Scholar 

  20. Matouk AE (2011) Chaos, feedback control and synchronization of a fractional-order modified autonomous Van der Pol-Duffing circuit. Commun Nonlinear Sci Numer Simul 16(2):975–986

    Google Scholar 

  21. Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824

    Google Scholar 

  22. Pehlivan I, Moroz IM, Vaidyanathan S (2014) Analysis, synchronization and circuit design of a novel butterfly attractor. J Sound Vib 333(20):5077–5096

    Article  Google Scholar 

  23. Pham VT, Volos CK, Vaidyanathan S, Le TP, Vu VY (2015) A memristor-based hyperchaotic system with hidden attractors: dynamics, synchronization and circuital emulating. J Eng Sci Technol Rev 8(2):205–214

    Google Scholar 

  24. Rasappan S, Vaidyanathan S (2012) Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control. Far East J Math Sci 67(2):265–287

    Google Scholar 

  25. Rasappan S, Vaidyanathan S (2012) Hybrid synchronization of n-scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback. Arch Control Sci 22(3):343–365

    Google Scholar 

  26. Rasappan S, Vaidyanathan S (2012) Synchronization of hyperchaotic Liu system via backstepping control with recursive feedback. Commun Comput Inf Sci 305:212–221

    Google Scholar 

  27. Rasappan S, Vaidyanathan S (2013) Hybrid synchronization of \(n\)-scroll chaotic Chua circuits using adaptive backstepping control design with recursive feedback. Malays J Math Sci 7(2):219–246

    MathSciNet  Google Scholar 

  28. Rasappan S, Vaidyanathan S (2014) Global chaos synchronization of WINDMI and Coullet chaotic systems using adaptive backstepping control design. Kyungpook Math J 54(1):293–320

    Google Scholar 

  29. Rhouma R, Belghith S (2011) Cryptanalysis of a chaos-based cryptosystem. Commun Nonlinear Sci Numer Simul 16(2):876–884

    Article  MathSciNet  MATH  Google Scholar 

  30. Rössler OE (1976) An equation for continuous chaos. Phys Lett A 57(5):397–398

    Article  Google Scholar 

  31. Sampath S, Vaidyanathan S, Volos CK, Pham VT (2015) An eight-term novel four-scroll chaotic system with cubic nonlinearity and its circuit simulation. J Eng Sci Technol Rev 8(2):1–6

    Google Scholar 

  32. Sarasu P, Sundarapandian V (2011) Active controller design for the generalized projective synchronization of four-scroll chaotic systems. Int J Syst Signal Control Eng Appl 4(2):26–33

    Google Scholar 

  33. Sarasu P, Sundarapandian V (2011) The generalized projective synchronization of hyperchaotic Lorenz and hyperchaotic Qi systems via active control. Int J Soft Comput 6(5):216–223

    Google Scholar 

  34. Sarasu P, Sundarapandian V (2012) Adaptive controller design for the generalized projective synchronization of 4-scroll systems. Int J Syst Signal Control Eng Appl 5(2):21–30

    Google Scholar 

  35. Sarasu P, Sundarapandian V (2012) Generalized projective synchronization of three-scroll chaotic systems via adaptive control. Eur J Sci Res 72(4):504–522

    Google Scholar 

  36. Sarasu P, Sundarapandian V (2012) Generalized projective synchronization of two-scroll systems via adaptive control. Int J Soft Comput 7(4):146–156

    Google Scholar 

  37. Shahverdiev EM, Shore KA (2009) Impact of modulated multiple optical feedback time delays on laser diode chaos synchronization. Opt Commun 282(17):3568–3572

    Article  Google Scholar 

  38. Sprott JC (1994) Some simple chaotic flows. Phys Rev E 50(2):647–650

    Article  MathSciNet  Google Scholar 

  39. Sundarapandian V (2010) Output regulation of the Lorenz attractor. Far East J Math Sci 42(2):289–299

    MathSciNet  MATH  Google Scholar 

  40. Sundarapandian V (2011) Output regulation of the Arneodo-Coullet chaotic system. Commun Comput Inf Sci 133:98–107

    Article  Google Scholar 

  41. Sundarapandian V (2013) Analysis and anti-synchronization of a novel chaotic system via active and adaptive controllers. J Eng Sci Technol Rev 6(4):45–52

    Google Scholar 

  42. Sundarapandian V, Karthikeyan R (2011) Anti-synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems by adaptive control. Int J Syst Signal Control Eng Appl 4(2):18–25

    Google Scholar 

  43. Sundarapandian V, Karthikeyan R (2011) Anti-synchronization of Lü and Pan chaotic systems by adaptive nonlinear control. Eur J Sci Res 64(1):94–106

    Google Scholar 

  44. Sundarapandian V, Karthikeyan R (2012) Adaptive anti-synchronization of uncertain Tigan and Li systems. J Eng Appl Sci 7(1):45–52

    Google Scholar 

  45. Sundarapandian V, Karthikeyan R (2012) Hybrid synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems via active control. J Eng Appl Sci 7(3):254–264

    Google Scholar 

  46. Sundarapandian V, Pehlivan I (2012) Analysis, control, synchronization, and circuit design of a novel chaotic system. Math Comput Modell 55(7–8):1904–1915

    Article  MathSciNet  MATH  Google Scholar 

  47. Sundarapandian V, Sivaperumal S (2011) Sliding controller design of hybrid synchronization of four-wing chaotic systems. Int J Soft Comput 6(5):224–231

    Article  Google Scholar 

  48. Suresh R, Sundarapandian V (2013) Global chaos synchronization of a family of \(n\)-scroll hyperchaotic Chua circuits using backstepping control with recursive feedback. Far East J Math Sci 73(1):73–95

    MATH  Google Scholar 

  49. Tigan G, Opris D (2008) Analysis of a 3D chaotic system. Chaos Solitons Fractals 36:1315–1319

    Google Scholar 

  50. Tuwankotta JM (2006) Chaos in a coupled oscillators system with widely spaced frequencies and energy-preserving non-linearity. Int J Non-Linear Mech 41(2):180–191

    Article  MathSciNet  MATH  Google Scholar 

  51. Usama M, Khan MK, Alghathbar K, Lee C (2010) Chaos-based secure satellite imagery cryptosystem. Comput Math Appl 60(2):326–337

    Article  MathSciNet  MATH  Google Scholar 

  52. Vaidyanathan S (2011) Hybrid chaos synchronization of Liu and Lü systems by active nonlinear control. Commun Comput Inf Sci 204:1–10

    Google Scholar 

  53. Vaidyanathan S (2011) Output regulation of the unified chaotic system. Commun Comput Inf Sci 204:84–93

    Google Scholar 

  54. Vaidyanathan S (2012) Analysis and synchronization of the hyperchaotic Yujun systems via sliding mode control. Adv Intell Syst Comput 176:329–337

    Google Scholar 

  55. Vaidyanathan S (2012) Anti-synchronization of Sprott-L and Sprott-M chaotic systems via adaptive control. Int J Control Theory Appl 5(1):41–59

    Google Scholar 

  56. Vaidyanathan S (2012) Global chaos control of hyperchaotic Liu system via sliding control method. Int J Control Theory Appl 5(2):117–123

    Google Scholar 

  57. Vaidyanathan S (2012) Output regulation of the Liu chaotic system. Appl Mech Mater 110–116:3982–3989

    Google Scholar 

  58. Vaidyanathan S (2012) Sliding mode control based global chaos control of Liu-Liu-Liu-Su chaotic system. Int J Control Theory Appl 5(1):15–20

    Google Scholar 

  59. Vaidyanathan S (2013) A new six-term 3-D chaotic system with an exponential nonlinearity. Far East J Math Sci 79(1):135–143

    Google Scholar 

  60. Vaidyanathan S (2013) 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

    Google Scholar 

  61. Vaidyanathan S (2013) Analysis, control and synchronization of hyperchaotic Zhou system via adaptive control. Adv Intell Syst Comput 177:1–10

    Google Scholar 

  62. Vaidyanathan S (2014) A new eight-term 3-D polynomial chaotic system with three quadratic nonlinearities. Far East J Math Sci 84(2):219–226

    Google Scholar 

  63. Vaidyanathan S (2014) Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities. Eur Phys J: Spec Top 223(8):1519–1529

    Google Scholar 

  64. Vaidyanathan S (2014) Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities. Int J Modell Identif Control 22(1):41–53

    Google Scholar 

  65. Vaidyanathan S (2014) Generalized projective synchronisation of novel 3-D chaotic systems with an exponential non-linearity via active and adaptive control. Int J Modell Identif Control 22(3):207–217

    Google Scholar 

  66. Vaidyanathan S (2014) Global chaos synchronization of identical Li-Wu chaotic systems via sliding mode control. Int J Modell Identif Control 22(2):170–177

    Google Scholar 

  67. Vaidyanathan S (2015) 3-cells cellular neural network (CNN) attractor and its adaptive biological control. Int J Pharm Tech Res 8(4):632–640

    Google Scholar 

  68. Vaidyanathan S (2015) A 3-D novel highly chaotic system with four quadratic nonlinearities, its adaptive control and anti-synchronization with unknown parameters. J Eng Sci Technol Rev 8(2):106–115

    Google Scholar 

  69. Vaidyanathan S (2015) A novel chemical chaotic reactor system and its adaptive control. Int J Chem Tech Res 8(7):146–158

    Google Scholar 

  70. Vaidyanathan S (2015) Adaptive backstepping control of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J Pharm Tech Res 8(2):256–261

    Google Scholar 

  71. Vaidyanathan S (2015) Adaptive biological control of generalized Lotka-Volterra three-species biological system. Int J Pharm Tech Res 8(4):622–631

    Google Scholar 

  72. Vaidyanathan S (2015) Adaptive chaotic synchronization of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J Pharm Tech Res 8(5):964–973

    Google Scholar 

  73. Vaidyanathan S (2015) Adaptive control of a chemical chaotic reactor. Int J Pharm Tech Res 8(3):377–382

    Google Scholar 

  74. Vaidyanathan S (2015) Adaptive control of the FitzHugh-Nagumo chaotic neuron model. Int J Pharm Tech Res 8(6):117–127

    Google Scholar 

  75. Vaidyanathan S (2015) Adaptive synchronization of chemical chaotic reactors. Int J Chem Tech Res 8(2):612–621

    Google Scholar 

  76. Vaidyanathan S (2015) Adaptive synchronization of generalized Lotka-Volterra three-species biological systems. Int J Pharm Tech Res 8(5):928–937

    Google Scholar 

  77. Vaidyanathan S (2015) Adaptive synchronization of novel 3-D chemical chaotic reactor systems. Int J Chem Tech Res 8(7):159–171

    Google Scholar 

  78. Vaidyanathan S (2015) Adaptive synchronization of the identical FitzHugh-Nagumo chaotic neuron models. Int J Pharm Tech Res 8(6):167–177

    Google Scholar 

  79. Vaidyanathan S (2015) Analysis, control, and synchronization of a 3-D novel jerk chaotic system with two quadratic nonlinearities. Kyungpook Math J 55:563–586

    Google Scholar 

  80. Vaidyanathan S (2015) Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity. Int J Modell Identif Control 23(2):164–172

    Google Scholar 

  81. Vaidyanathan S (2015) Anti-synchronization of Brusselator chemical reaction systems via adaptive control. Int J Chem Tech Res 8(6):759–768

    Google Scholar 

  82. Vaidyanathan S (2015) Chaos in neurons and adaptive control of Birkhoff-Shaw strange chaotic attractor. Int J Pharm Tech Res 8(5):956–963

    Google Scholar 

  83. Vaidyanathan S (2015) Chaos in neurons and synchronization of Birkhoff-Shaw strange chaotic attractors via adaptive control. Int J Pharm Tech Res 8(6):1–11

    Google Scholar 

  84. Vaidyanathan S (2015) Coleman-Gomatam logarithmic competitive biology models and their ecological monitoring. Int J Pharm Tech Res 8(6):94–105

    Google Scholar 

  85. Vaidyanathan S (2015) Dynamics and control of Brusselator chemical reaction. Int J Chem Tech Res 8(6):740–749

    Google Scholar 

  86. Vaidyanathan S (2015) Dynamics and control of Tokamak system with symmetric and magnetically confined plasma. Int J Chem Tech Res 8(6):795–803

    Google Scholar 

  87. Vaidyanathan S (2015) Global chaos synchronization of chemical chaotic reactors via novel sliding mode control method. Int J Chem Tech Res 8(7):209–221

    Google Scholar 

  88. Vaidyanathan S (2015) Global chaos synchronization of the forced Van der Pol chaotic oscillators via adaptive control method. Int J Pharm Tech Res 8(6):156–166

    Google Scholar 

  89. Vaidyanathan S (2015) Global chaos synchronization of the Lotka-Volterra biological systems with four competitive species via active control. Int J Pharm Tech Res 8(6):206–217

    Google Scholar 

  90. Vaidyanathan S (2015) Lotka-Volterra population biology models with negative feedback and their ecological monitoring. Int J Pharm Tech Res 8(5):974–981

    Google Scholar 

  91. Vaidyanathan S (2015) Lotka-Volterra two species competitive biology models and their ecological monitoring. Int J Pharm Tech Res 8(6):32–44

    Google Scholar 

  92. Vaidyanathan S (2015) Output regulation of the forced Van der Pol chaotic oscillator via adaptive control method. Int J Pharm Tech Res 8(6):106–116

    Google Scholar 

  93. Vaidyanathan S, Azar AT (2015) Analysis and control of a 4-D novel hyperchaotic system. In: Azar AT, Vaidyanathan S (eds) Chaos modeling and control systems design, vol 581. Studies in computational intelligence. Springer, Germany, pp 19–38

    Google Scholar 

  94. Vaidyanathan S, Azar AT (2015) Analysis, control and synchronization of a nine-term 3-D novel chaotic system. In: Azar AT, Vaidyanathan S (eds) Chaos modelling and control systems design. Studies in computational intelligence, vol 581. Springer, Germany, pp 19–38

    Google Scholar 

  95. Vaidyanathan S, Azar AT (2015) Anti-synchronization of identical chaotic systems using sliding mode control and an application to Vaidhyanathan-Madhavan chaotic systems. Stud Comput Intell 576:527–547

    Google Scholar 

  96. Vaidyanathan S, Azar AT (2015) Hybrid synchronization of identical chaotic systems using sliding mode control and an application to Vaidhyanathan chaotic systems. Stud Comput Intell 576:549–569

    Google Scholar 

  97. Vaidyanathan S, Madhavan K (2013) Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system. Int J Control Theory Appl 6(2):121–137

    Google Scholar 

  98. Vaidyanathan S, Pakiriswamy S (2013) Generalized projective synchronization of six-term Sundarapandian chaotic systems by adaptive control. Int J Control Theory Appl 6(2):153–163

    Google Scholar 

  99. Vaidyanathan S, Pakiriswamy S (2015) A 3-D novel conservative chaotic system and its generalized projective synchronization via adaptive control. J Eng Sci Technol Rev 8(2):52–60

    Google Scholar 

  100. Vaidyanathan S, Rajagopal K (2011) Anti-synchronization of Li and T chaotic systems by active nonlinear control. Commun Comput Inf Sci 198:175–184

    Google Scholar 

  101. Vaidyanathan S, Rajagopal K (2011) Global chaos synchronization of hyperchaotic Pang and Wang systems by active nonlinear control. Commun Comput Inf Sci 204:84–93

    Google Scholar 

  102. Vaidyanathan S, Rajagopal K (2011) Global chaos synchronization of Lü and Pan systems by adaptive nonlinear control. Commun Comput Inf Sci 205:193–202

    Google Scholar 

  103. Vaidyanathan S, Rajagopal K (2012) Global chaos synchronization of hyperchaotic Pang and hyperchaotic Wang systems via adaptive control. Int J Soft Comput 7(1):28–37

    Article  MATH  Google Scholar 

  104. Vaidyanathan S, Rasappan S (2011) Global chaos synchronization of hyperchaotic Bao and Xu systems by active nonlinear control. Commun Comput Inf Sci 198:10–17

    Article  Google Scholar 

  105. Vaidyanathan S, Rasappan S (2014) Global chaos synchronization of \(n\)-scroll Chua circuit and Lur’e system using backstepping control design with recursive feedback. Arab J Sci Eng 39(4):3351–3364

    Article  Google Scholar 

  106. Vaidyanathan S, Sampath S (2011) Global chaos synchronization of hyperchaotic Lorenz systems by sliding mode control. Commun Comput Inf Sci 205:156–164

    Article  Google Scholar 

  107. Vaidyanathan S, Sampath S (2012) Anti-synchronization of four-wing chaotic systems via sliding mode control. Int J Autom Comput 9(3):274–279

    Article  Google Scholar 

  108. Vaidyanathan S, Volos C (2015) Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system. Arch Control Sci 25(3):333–353

    Google Scholar 

  109. Vaidyanathan S, Volos C, Pham VT (2014) Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation. Arch Control Sci 24(4):409–446

    Google Scholar 

  110. Vaidyanathan S, Volos C, Pham VT (2014) Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation. Arch Control Sci 24(4):409–446

    Google Scholar 

  111. Vaidyanathan S, Volos C, Pham VT, Madhavan K, Idowu BA (2014) Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities. Arch Control Sci 24(3):375–403

    Google Scholar 

  112. Vaidyanathan S, Idowu BA, Azar AT (2015) Backstepping controller design for the global chaos synchronization of Sprott’s jerk systems. Stud Comput Intell 581:39–58

    Google Scholar 

  113. Vaidyanathan S, Rajagopal K, Volos CK, Kyprianidis IM, Stouboulos IN (2015) Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in LabVIEW. J Eng Sci Technol Rev 8(2):130–141

    Google Scholar 

  114. Vaidyanathan S, Volos C, Pham VT, Madhavan K (2015) Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation. Arch Control Sci 25(1):5–28

    Google Scholar 

  115. Vaidyanathan S, Volos CK, Kyprianidis IM, Stouboulos IN, Pham VT (2015) Analysis, adaptive control and anti-synchronization of a six-term novel jerk chaotic system with two exponential nonlinearities and its circuit simulation. J Eng Sci Technol Rev 8(2):24–36

    Google Scholar 

  116. Vaidyanathan S, Volos CK, Madhavan K (2015) Analysis, control, synchronization and SPICE implementation of a novel 4-D hyperchaotic Rikitake dynamo system without equilibrium. J Eng Sci Technol Rev 8(2):232–244

    Google Scholar 

  117. Vaidyanathan S, Volos CK, Pham VT (2015) Analysis, adaptive control and adaptive synchronization of a nine-term novel 3-D chaotic system with four quadratic nonlinearities and its circuit simulation. J Eng Sci Technol Rev 8(2):181–191

    Google Scholar 

  118. Vaidyanathan S, Volos CK, Pham VT (2015) Global chaos control of a novel nine-term chaotic system via sliding mode control. In: Azar AT, Zhu Q (eds) Advances and applications in sliding mode control systems, vol 576. Studies in computational intelligence. Springer, Germany, pp 571–590

    Google Scholar 

  119. Vaidyanathan S, Volos CK, Pham VT, Madhavan K (2015) Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation. Arch Control Sci 25(1):135–158

    Google Scholar 

  120. Vaidyanathan S, Volos CK, Rajagopal K, Kyprianidis IM, Stouboulos IN (2015) Adaptive backstepping controller design for the anti-synchronization of identical WINDMI chaotic systems with unknown parameters and its SPICE implementation. J Eng Sci Technol Rev 8(2):74–82

    Google Scholar 

  121. Volos CK, Kyprianidis IM, Stouboulos IN, Anagnostopoulos AN (2009) Experimental study of the dynamic behavior of a double scroll circuit. J Appl Funct Anal 4:703–711

    Google Scholar 

  122. Volos CK, Kyprianidis IM, Stouboulos IN (2013) Experimental investigation on coverage performance of a chaotic autonomous mobile robot. Robot Auton Syst 61(12):1314–1322

    Article  Google Scholar 

  123. Volos CK, Kyprianidis IM, Stouboulos IN, Tlelo-Cuautle E, Vaidyanathan S (2015) Memristor: a new concept in synchronization of coupled neuromorphic circuits. J Eng Sci Technol Rev 8(2):157–173

    Google Scholar 

  124. Wang X, Ge C (2008) Controlling and tracking of Newton-Leipnik system via backstepping design. Int J Nonlinear Sci 5(2):133–139

    MathSciNet  MATH  Google Scholar 

  125. Wei Z, Yang Q (2010) Anti-control of Hopf bifurcation in the new chaotic system with two stable node-foci. Appl Math Comput 217(1):422–429

    MathSciNet  MATH  Google Scholar 

  126. Xiao X, Zhou L, Zhang Z (2014) Synchronization of chaotic Lur’e systems with quantized sampled-data controller. Commun Nonlinear Sci Numer Simul 19(6):2039–2047

    Article  MathSciNet  Google Scholar 

  127. Yang J, Zhu F (2013) Synchronization for chaotic systems and chaos-based secure communications via both reduced-order and step-by-step sliding mode observers. Commun Nonlinear Sci Numer Simul 18(4):926–937

    Article  MathSciNet  MATH  Google Scholar 

  128. Yang J, Chen Y, Zhu F (2014) Singular reduced-order observer-based synchronization for uncertain chaotic systems subject to channel disturbance and chaos-based secure communication. Appl Math Comput 229:227–238

    Google Scholar 

  129. Zhang H, Zhou J (2012) Synchronization of sampled-data coupled harmonic oscillators with control inputs missing. Syst Control Lett 61(12):1277–1285

    Article  MathSciNet  MATH  Google Scholar 

  130. Zhou W, Xu Y, Lu H, Pan L (2008) On dynamics analysis of a new chaotic attractor. Phys Lett A 372(36):5773–5777

    Article  MathSciNet  MATH  Google Scholar 

  131. Zhu C, Liu Y, Guo Y (2010) Theoretic and numerical study of a new chaotic system. Intell Inf Manag 2:104–109

    Google Scholar 

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  1. Research and Development Centre, Vel Tech University, Avadi, Chennai, 600062, Tamil Nadu, India

    Sundarapandian Vaidyanathan

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  1. Research and Development Centre, Vel Tech University, Chennai, India

    Sundarapandian Vaidyanathan

  2. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Christos Volos

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Vaidyanathan, S. (2016). Adaptive Control and Synchronization of a Rod-Type Plasma Torch Chaotic System via Backstepping Control Method. In: Vaidyanathan, S., Volos, C. (eds) Advances and Applications in Chaotic Systems . Studies in Computational Intelligence, vol 636. Springer, Cham. https://doi.org/10.1007/978-3-319-30279-9_24

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  • DOI: https://doi.org/10.1007/978-3-319-30279-9_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30278-2

  • Online ISBN: 978-3-319-30279-9

  • eBook Packages: EngineeringEngineering (R0)

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