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Synchronization of general chaotic systems using neural controllers with application to secure communication

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Abstract

The main contribution of this paper is to propose a nonlinear robust controller to synchronize general chaotic systems, such that the controller does not need the information of the chaotic system’s model. Following this purpose, in this paper, two methods are proposed to synchronize general forms of chaotic systems with application in secure communication. The first method uses radial basis function neural network (RBFNN) as a controller. All the parameters of the RBFNN are derived and optimized via particle swarm optimization (PSO) algorithm and genetic algorithm (GA). In order to increase the robustness of the controller, in the second method, an integral term is added to the RBF neural network gives an integral RBFNN (IRBFNN). The coefficients of the integral term and the parameters of IRBFNN are also derived and optimized via PSO and GA. The proposed methods are applied to the famous Lorenz chaotic system for secure communication. The performance and control effort of the proposed methods are compared with the recently proposed PID controller optimized via GA. Simulation results show the superiority of the proposed methods in comparison to the recent one in improving synchronization while using smaller control effort.

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References

  1. Yang T (2004) A survey of chaotic secure communication systems. Int J Comput Cogn 2:81–130

    Google Scholar 

  2. Lin S-L, Tung P-C (2009) A new method for chaos control in communication systems. Chaos Solitons Fractals 42:3234–3241

    Article  MATH  Google Scholar 

  3. Lin J-S, Huang C-F, Liao T-L, Yan J–J (2010) Design and implementation of digital secure communication based on synchronized chaotic systems. Digital Signal Process 20:229–237

    Article  MATH  Google Scholar 

  4. Wang H, Zhu X-J, Gao S-W, Chen Z-Y (2010) Singular observer approach for chaotic synchronization and private communication. Commun Nonlinear Sci Numer Simul (in press), doi:10.1016/j.cnsns.2010.06.021

  5. Halle K, Wu CW, Itoh M, Chua LO (1993) Spread spectrum communication through modulation of chaos. IEICE Trans Commun 3:469–477

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Liu S-Y, Yu X, Zhu S-J (2008) Study on the chaos anti-control technology in nonlinear vibration isolation system. J Sound Vibrat 310:855–864

    Article  Google Scholar 

  8. Ott E, Grebogi C, York JA (1990) Controlling chaos. Phys Rev Lett 64:1196–1199

    Article  MathSciNet  MATH  Google Scholar 

  9. Hu G, Pivka L, Zheleznyak AL (1995) Synchronization of a one-dimensional array of Chua’s circuits by feedback control and noise. IEEE Trans Circuits Syst I Fundament Theory Appl 42:736–740

    Article  Google Scholar 

  10. Jiang GP, Chen GR, Tang WK (2003) A new criterion for chaos synchronization using linear state feedback control. Int J Bifurc Chaos 13:2343–2351

    Article  MATH  Google Scholar 

  11. Schmitz R (2001) Use of chaotic dynamical systems in cryptography. J Franklin Inst 338:429–441

    Article  MathSciNet  MATH  Google Scholar 

  12. Efimov DV (2006) Dynamical adaptive synchronization. Int J Adapt Control Signal Process 20:491–507

    Article  MathSciNet  MATH  Google Scholar 

  13. Loria A, Zavala-Rio A (2007) Adaptive tracking control of chaotic systems with applications to synchronization. IEEE Trans Circuits Syst I Regular Pap 54:2019–2029

    Article  MathSciNet  Google Scholar 

  14. Lin J-S, Yan J–J (2009) Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller. Nonlinear Anal Real World Appl 10:1151–1159

    Article  MathSciNet  MATH  Google Scholar 

  15. Li R-H (2009) Exponential generalized synchronization of uncertain coupled chaotic systems by adaptive control. Commun Nonlinear Sci Numer Simul 14:2757–2764

    Article  MathSciNet  MATH  Google Scholar 

  16. Salarieh H, Alasti A (2009) Adaptive synchronization of two chaotic systems with stochastic unknown parameters. Commun Nonlinear Sci Numer Simul 14:508–519

    Article  MathSciNet  MATH  Google Scholar 

  17. Tian YP, Yu X (2000) Stabilizing unstable periodic orbits of chaotic systems via an optimal principle. J Franklin Inst 337:771–779

    Article  MathSciNet  MATH  Google Scholar 

  18. Kuo H–H, Hou Y–Y, Yan J–J, Liao T-L (2009) Reliable synchronization of nonlinear chaotic systems. Math Comput Simulat 79:1627–1635

    Article  MathSciNet  MATH  Google Scholar 

  19. Grzybowski JMV, Rafikov M, Balthazar JM (2009) Synchronization of the unified chaotic system and application in secure communication. Commun Nonlinear Sci Numer Simul 14:2793–2806

    Article  MathSciNet  MATH  Google Scholar 

  20. Morgül Ö, Akgül M (2002) A switching synchronization scheme for a class of chaotic systems. Phys Lett A 301:241–249

    Article  MathSciNet  MATH  Google Scholar 

  21. Millerioux G, Daafouz J (2003) An observer-based approach for input-independent global chaos synchronization of discrete-time switched systems. IEEE Trans Circuits Syst I Fundament Theory Appl 50:1270–1279

    Article  MathSciNet  Google Scholar 

  22. Stojanovski T, Kocarev L, Parlitz U (1996) Driving and synchronizing by chaotic impulses. Phys Rev E 54:2128–2131

    Article  Google Scholar 

  23. Yang T, Chua LO (1997) Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans Circuits Syst I Fundament Theory Appl 44:976–988

    Article  MathSciNet  Google Scholar 

  24. Li ZG, Wen CY, Soh YC, Xie WX (2001) The stabilization and synchronization of Chua’s oscillators via impulsive control. IEEE Trans Circuits Syst I Fundament Theory Appl 48:1351–1355

    Article  MathSciNet  MATH  Google Scholar 

  25. Zheng Y, Chen G (2009) Fuzzy impulsive control of chaotic systems based on TS fuzzy model. Chaos Solitons Fractals 39:2002–2011

    Article  MathSciNet  MATH  Google Scholar 

  26. Morgül Ö, Feki M (1997) Synchronization of chaotic systems by using occasional coupling. Phys Rev E 55:5004–5010

    Article  MathSciNet  Google Scholar 

  27. Li CD, Feng G, Liao XF (2007) Stabilization of nonlinear systems via periodically intermittent control. IEEE Trans Circuits Syst II Express Briefs 54:1019–1023

    Article  Google Scholar 

  28. Huang TW, Li CD, Yu WW, Chen GR (2009) Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback. Nonlinearity 22:569–584

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhu H, Cui B (2010) Stabilization and synchronization of chaotic systems via intermittent control. Commun Nonlinear Sci Numer Simul 15:3577–3586

    Article  MathSciNet  MATH  Google Scholar 

  30. Guo SM, Shieh LS, Chen G, Lin CF (2000) Effective chaotic orbit tracker: a prediction-based digital redesign approach. IEEE Trans Circuits Syst I Fundament Theory Appl 47:1557–1570

    Article  MathSciNet  MATH  Google Scholar 

  31. Wu T, Chen MS (2002) Chaos control of the modified Chua’s circuit system. Phys D 164:53–58

    Article  MathSciNet  MATH  Google Scholar 

  32. Zhang J, Li C, Zhang H, Yu J (2004) Chaos synchronization using single variable feedback based on backstepping method. Chaos Solitons Fractals 21:1183–1193

    Article  MathSciNet  MATH  Google Scholar 

  33. Lin D, Wang X, Nian F, Zhang Y (2010) Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems. Neurocomputing 73:2873–2881

    Article  Google Scholar 

  34. Yan JJ, Hung ML, Chiang TY, Yang YS (2006) Robust synchronization of chaotic systems via adaptive sliding mode control. Phys Lett A 356:220–225

    Article  MATH  Google Scholar 

  35. Wang H, Han ZZ, Xie QY, Zhang W (2009) Finite-time chaos control via nonsingular terminal sliding mode control. Commun Nonlinear Sci Numer Simulat 14:2728–2733

    Article  MathSciNet  MATH  Google Scholar 

  36. Wang H, Han ZZ, Xie QY, Zhang W (2009) Sliding mode control for chaotic systems based on LMI. Commun Nonlinear Sci Numer Simulat 14:1410–1417

    Article  MathSciNet  MATH  Google Scholar 

  37. Mou C, Jiang C-S, Bin J, Wu Q-X (2009) Sliding mode synchronization controller design with neural network for uncertain chaotic systems. Chaos Solitons Fractals 39:1856–1863

    Article  MATH  Google Scholar 

  38. Xiang W, Huangpu Y (2010) Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties. Commun Nonlinear Sci Numer Simulat 15:3241–3247

    Article  MathSciNet  MATH  Google Scholar 

  39. Pourmahmood M, Khanmohammadi S, Alizadeh G (2011) Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller. Commun Nonlinear Sci Numer Simulat 16:2853–2868

    Article  MathSciNet  MATH  Google Scholar 

  40. Lin T-C, Chen M-C, Roopaei M (2011) Synchronization of uncertain chaotic systems based on adaptive type-2 fuzzy sliding mode control. Eng Appl Artif Intell 24:39–49

    Article  Google Scholar 

  41. Wang F, Liu C (2007) Synchronization of unified chaotic system based on passive control. Phys D 225:55–60

    Article  MathSciNet  MATH  Google Scholar 

  42. Zhang H, Ma X (2004) Synchronization of uncertain chaotic systems with parameters perturbation via active control. Chaos Solitons Fractals 21:39–47

    Article  MathSciNet  MATH  Google Scholar 

  43. Lee SM, Ji DH, Park JH, Won SC (2008) H∞ synchronization of chaotic systems via dynamic feedback approach. Phys Lett A 372:4905–4912

    Article  MathSciNet  MATH  Google Scholar 

  44. Kim J-H, Park C-W, Kim E, Park M (2005) Fuzzy adaptive synchronization of uncertain chaotic systems. Phys Lett A 334:295–305

    Article  MathSciNet  MATH  Google Scholar 

  45. Hyun C-H, Kim J-H, Kim E, Park M (2006) Adaptive fuzzy observer based synchronization design and secure communications of chaotic systems. Chaos Solitons Fractals 27:930–940

    Article  MathSciNet  MATH  Google Scholar 

  46. Yau H-T, Shieh C-S (2008) Chaos synchronization using fuzzy logic controller. Nonlinear Anal Real World Appl 9:1800–1810

    Article  MathSciNet  MATH  Google Scholar 

  47. Zhang L, Huang L, Zhang Z, Wang Z (2008) Fuzzy adaptive synchronization of uncertain chaotic systems via delayed feedback control. Phys Lett A 372:6082–6086

    Article  MATH  Google Scholar 

  48. Hwang E, Hyun C, Kim E, Park M (2009) Fuzzy model based adaptive synchronization of uncertain chaotic systems: robust tracking control approach. Phys Lett A 373:1935–1939

    Article  MATH  Google Scholar 

  49. Li S-Y, Ge Z-M (2011) Generalized synchronization of chaotic systems with different orders by fuzzy logic constant controller. Exp Syst Appl 38:2302–2310

    Article  Google Scholar 

  50. Yin C, Zhong S-M, Chen W-F (2011) Design PD controller for master–slave synchronization of chaotic Lur’e systems with sector and slope restricted nonlinearities. Commun Nonlinear Sci Numer Simulat 16:1632–1639

    Article  MathSciNet  MATH  Google Scholar 

  51. Chen HC, Chang JF, Yan JJ, Liao TL (2008) EP-based PID control design for chaotic synchronization with application in secure communication. Exp Syst Appl 34:1169–1177

    Article  Google Scholar 

  52. Coelho LS, Bernert DLA (2009) PID control design for chaotic synchronization using a Tribes optimization approach. Chaos Solitons Fractals 42:634–640

    Article  Google Scholar 

  53. Coelho LS, Grebogi RB (2010) Chaotic synchronization using PID control combined with population based incremental learning algorithm. Exp Syst Appl 37:5347–5352

    Article  Google Scholar 

  54. Coelho LS, Bernert DLA (2010) A modified ant colony optimization algorithm based on differential evolution for chaotic synchronization. Exp Syst Appl 37:4198–4203

    Article  Google Scholar 

  55. Ren H, Liu D (2007) Synchronization of chaos using radial basis functions neural networks. J Syst Eng Electron 18:83–88

    Article  Google Scholar 

  56. Hsu C-F, Chung C-M, Lin C-M, Hsu C-Y (2009) Adaptive CMAC neural control of chaotic systems with a PI-type learning algorithm. Exp Syst Appl 36:11836–11843

    Article  Google Scholar 

  57. Chen M, Chen W (2009) Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems. Chaos Solitons Fractals 41:2716–2724

    Article  MATH  Google Scholar 

  58. Chen C-H, Lin C-M, Li M-C (2011) Development of PI training algorithms for neuro-wavelet control on the synchronization of uncertain chaotic systems. Neurocomputing (in press), doi:10.1016/j.neucom.2011.03.045

  59. Chen C-S, Chen H–H (2009) Robust adaptive neural-fuzzy-network control for the synchronization of uncertain chaotic systems. Nonlinear Anal Real World Appl 10:1466–1479

    Article  MathSciNet  MATH  Google Scholar 

  60. Chen C-S (2009) Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems. Exp Syst Appl 36:11827–11835

    Article  Google Scholar 

  61. Lin D, Wang X (2011) Self-organizing adaptive fuzzy neural control for the synchronization of uncertain chaotic systems with random-varying parameters. Neurocomputing 74:2241–2249

    Article  Google Scholar 

  62. Hsu C-F (2011) Adaptive fuzzy wavelet neural controller design for chaos synchronization. Exp Syst Appl 38:10475–10483

    Article  Google Scholar 

  63. Sztipanovits J, Waknis P (1991) System identification with neural network controlled resonator-banks. In: The proceedings of the IEEE international symposium on intelligent control, pp 158–163

  64. Wang Y-J, Lin C-T (1998) Runge-Kutta neural network for identification of dynamical systems in high accuracy. IEEE Trans Neural Netw 9:294–307

    Article  Google Scholar 

  65. Shieh C-S, Lin C-T (2002) A vector neural network for emitter identification. IEEE Trans Antennas Propagat 50:1120–1127

    Article  Google Scholar 

  66. Sheikhan M, Tabataba Vakili V, Garoucy S (2009) Complexity reduction of LD-CELP speech coding in prediction of gain using neural networks. World Appl Sci J 7 (Special Issue of Computer & IT):38–44

  67. Monjezi M, Ahmadi M, Sheikhan M, Bahrami A, Salimi AR (2010) Predicting blast-induced ground vibration using various types of neural networks. Soil Dyn Earthq Eng 30:1233–1236

    Article  Google Scholar 

  68. Sheikhan M, Hatami Sadegh M (2010) Blind estimation of signal to noise ratio using time-delay radial basis connectionist models. World Appl Sci J 8:296–301

    Google Scholar 

  69. Sheikhan M, Garoucy S (2011) Prediction of gain in LD-CELP using hybrid genetic/PSO-neural models. J Adv Res Comput 1(3):1–12

    Google Scholar 

  70. Ming-Chuan Y, Pariseau B, Jenkins JM, DiCarlo LA (1994) Intracardiac arrhythmia classification using neural networks and time-frequency analysis. In: The proceedings of the IEEE workshop on computers in cardiology, pp 449–452

  71. Zahorian SA, Nossair ZB (1999) A partitioned neural network approach for vowel classification using smoothed time/frequency features. IEEE Trans Speech Audio Process 7:414–425

    Google Scholar 

  72. Sexton RS, Dorsey RE (2000) Reliable classification using neural networks: a genetic algorithm and backpropagation comparison. Decis Support Syst 30:11–22

    Article  Google Scholar 

  73. Kaefer F, Heilman CM, Ramenofsky SD (2005) A neural network application to consumer classification to improve the timing of direct marketing activities. Comput Oper Res 32:414–425

    Article  Google Scholar 

  74. Sheikhan M, Jadidi Z (2009) Misuse detection using hybrid of association rule mining and connectionist modeling. World Appl Sci J 7 (Special Issue of Computer & IT):31–37

  75. Sheikhan M, Sha’bani AA (2009) Fast neural intrusion detection system based on hidden weight optimization algorithm and feature selection. World Appl Sci J 7 (Special Issue of Computer & IT):45–53

  76. Sheikhan M, Jadidi Z, Beheshti M (2010) Effects of feature reduction on the performance of attack recognition by static and dynamic neural networks. World Appl Sci J 8:302–308

    Google Scholar 

  77. Sheikhan M, Jadidi Z, Farrokhi A (2010) Intrusion detection using reduced-size RNN based on feature grouping. Neural Comput Appl (in Press), doi:10.1007/s00521-010-0487-0)

  78. Sheikhan M, Khalili A (2010) Intrusion detection based on rule extraction from dynamic cell structure neural network. Majlesi J Electric Eng 4(4):24–34

    Google Scholar 

  79. Gharavian D, Sheikhan M, Nazerieh AR, Garoucy S (2011) Speech emotion recognition using FCBF feature selection method and GA-optimized fuzzy ARTMAP neural network. Neural Comput Appl (in press), doi:10.1007/s00521-011-0643-1

  80. Ko WL, Mittra R (1995) Conductivity estimation by neural network. In: The proceedings of the international symposium of antennas and propagation society, vol 4, pp 1860–1863

  81. Chinman RB, Ding J (1998) Prediction limit estimation for neural network models. IEEE Trans Neural Netw 9:1515–1522

    Google Scholar 

  82. Langley CS, D’Eleuterio GMT (2001) Neural network-based pose estimation for fixtureless assembly. In: The proceedings of the IEEE international symposium on computational intelligence in robotics and automation, pp 248–253

  83. Sheikhan M, Gharavian D, Ashoftedel F (2011) Using DTW-neural based MFCC warping to improve emotional speech recognition. Neural Comput Appl (in press), doi:10.1007/s00521-011-0620-8

  84. Katijani Y, Hipel WK, McLeod AI (2005) Forecasting nonlinear time series with feedforward neural networks: a case study of Canadian lynx data. J Forecast 24:105–117

    Article  MathSciNet  Google Scholar 

  85. Sheikhan M, Movaghar B (2009) Exchange rate prediction using an evolutionary connectionist model. World Appl Sci J 7(Special Issue of Computer & IT):8–16

  86. Sheikhan M, Mohammadi N (2011) Neural-based electricity load forecasting using hybrid of GA and ACO for feature selection. Neural Comput Appl (in press), doi:10.1007/s00521-011-0599-1

  87. Hopfield JJ, Tank DW (1985) Neural computation of decisions in optimization problems. Biol Cybern 52:141–152

    MathSciNet  MATH  Google Scholar 

  88. Wang L, Liu W, Shi H (2009) Delay-constrained multicast routing using the noisy chaotic neural networks. IEEE Trans Comput 58:82–89

    Article  MathSciNet  Google Scholar 

  89. Sheikhan M, Hemmati E (2011) Transient chaotic neural network-based disjoint multipath routing for mobile ad-hoc networks. Neural Comput Appl (in press), doi:10.1007/s00521-011-0594-6

  90. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: The proceedings of the IEEE international conference on neural networks, pp 1942–1948

  91. Chee CY, Xu D (2005) Secure digital communication using controlled projective synchronization of chaos. Chaos Solitons Fractals 23:1063–1070

    MATH  Google Scholar 

  92. Zhu F (2009) Observer-based synchronization of uncertain chaotic system and its application to secure communications. Chaos Solitons Fractals 40:2384–2391

    Article  MATH  Google Scholar 

  93. Kolumbán G, Kennedy MP, Chua LO (1997) The role of synchronization in digital communication using chaos I. fundamentals of digital communications. IEEE Trans Circuits Syst I Fundament Theory Appl 44:927–936

    Article  Google Scholar 

  94. Bai EW, Lonngren KE, Uçar A (2005) Secure communication via multiple parameter modulation in a delayed chaotic system. Chaos Solitons Fractals 23:1071–1076

    MATH  Google Scholar 

  95. Wang XY, Wang M-J (2009) A chaotic secure communication scheme based on observer. Commun Nonlinear Sci Numer Simulat 14:1502–1508

    Article  Google Scholar 

  96. Chang W-D (2009) Digital secure communication via chaotic systems. Digital Signal Process 19:693–699

    Article  Google Scholar 

  97. Wu X-J, Wang H, Lu H-T (2011) Hyperchaotic secure communication via generalized function projective synchronization. Nonlinear Anal Real World Appl 12:1288–1299

    Article  MathSciNet  MATH  Google Scholar 

  98. Li D, Wang Z, Zhou J, Fang J, Ni J (2008) A note on chaotic synchronization of time-delay secure communication systems. Chaos Solitons Fractals 38:1217–1224

    Article  MathSciNet  MATH  Google Scholar 

  99. Lee S-H, Kapila V, Porfiri M, Panda A (2010) Master-slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators. Commun Nonlinear Sci Numer Simulat 15:4100–4113

    Article  MathSciNet  MATH  Google Scholar 

  100. Hyun C-H, Park C-W, Kim J-H, Park M (2009) Synchronization and secure communication of chaotic systems via robust adaptive high-gain fuzzy observer. Chaos Solitons Fractals 40:2200–2209

    Article  MathSciNet  MATH  Google Scholar 

  101. Yeh J-P, Wu K-L (2008) A simple method to synchronize chaotic systems and its application to secure communication. Math Comput Modell 47:894–902

    Article  MathSciNet  MATH  Google Scholar 

  102. Wang H, Han Z-H, Xie Q-Y, Zhang W (2009) Finite-time chaos synchronization of unified chaotic system with uncertain parameters. Commun Nonlinear Sci Numer Simulat 14:2239–2247

    Article  Google Scholar 

  103. Nana B, Woafo P (2011) Synchronized states in a ring of four mutually coupled oscillators and experimental application to secure communications. Commun Nonlinear Sci Numer Simulat 16:1725–1733

    Article  MathSciNet  MATH  Google Scholar 

  104. Changchien S-K, Huang C-K, Nien H–H, Shieh H-W (2009) Synchronization of the chaotic secure communication system with output state delay. Chaos Solitons Fractals 39:1578–1587

    Article  MathSciNet  MATH  Google Scholar 

  105. Xingyuan W, Bing X, Huaguang Z (2010) A multi-ary number communication system based on hyperchaotic system of 6th-order cellular neural network. Commun Nonlinear Sci Numer Simulat 15:124–133

    Article  Google Scholar 

  106. Coelho LS, Bernert DLA (2009) An improved harmony search algorithm for synchronization of discrete-time chaotic systems. Chaos Solitons Fractals 41:2526–2532

    Article  MATH  Google Scholar 

  107. Chang W-D (2009) PID control for chaotic synchronization using particle swarm optimization. Chaos Solitons Fractals 39:910–917

    Article  MATH  Google Scholar 

  108. Jahromi Shirazi M, Vatankhah R, Boroushaki M, Salarieh H, Alasty A (2011) Application of particle swarm optimization in chaos synchronization in noisy environment in presence of unknown parameter uncertainty. Commun Nonlinear Sci Numer Simulat (in press), doi:10.1016/j.cnsns.2011.05.032

  109. Modares H, Alfi A, Fateh MM (2010) Parameter identification of chaotic dynamic systems through an improved particle swarm optimization. Exp Syst Appl 37:3714–3720

    Article  Google Scholar 

  110. Cuomo KM, Oppenheim AV, Strogatz SH (1993) Synchronisation of Lorenz-based chaotic circuits with applications to communications. IEEE Trans Circuits Syst 40:626–633

    Google Scholar 

  111. Yu W (1999) Passive equivalence of chaos in Lorenz system. IEEE Trans Circuits Syst I Fundament Theory Appl 46:876–878

    Article  Google Scholar 

  112. Bai E-W, Lonngren KE (2000) Sequential synchronization of two Lorenz systems using active control. Chaos Solitons Fractals 11:1041–1044

    Article  MATH  Google Scholar 

  113. Ueta T, Chen G (2000) Bifurcation analysis of Chen’s attractor. Int J Bifurc Chaos 10:1917–1931

    MathSciNet  MATH  Google Scholar 

  114. Wang Y, Guan ZH, Wang HO (2003) Feedback an adaptive control for the synchronization of Chen system via a single variable. Phys Lett A 312:34–40

    Article  MathSciNet  MATH  Google Scholar 

  115. Xu WG, Shen HZ, Hu DP, Lei AZ (2005) Impulse tuning of Chua chaos. Int J Eng Sci 43:275–280

    Article  MATH  Google Scholar 

  116. Rafikov M, Balthazar JM (2004) On an optimal control design for Rössler system. Phys Lett A 333:241–245

    Article  MathSciNet  MATH  Google Scholar 

  117. Hua CC, Guan X, Li X, Shi P (2004) Adaptive observer-based control for a class of chaotic systems. Chaos Solitons Fractals 22:103–110

    Article  MathSciNet  MATH  Google Scholar 

  118. Goldberg DE (1989) Genetic algorithms in search optimization and learning. Addison Wesley, Reading

  119. Shi Y, Eberhart RC (1998) Parameter selection in particle swarm optimization. In: The proceedings of the international conference on evolutionary programming, pp 591–600

  120. Chen S, Billings SA, Cowan CFN, Grant PW (1990) Practical identification of Narmax models using radial basis functions. Int J Control 52:1327–1350

    Article  MathSciNet  MATH  Google Scholar 

  121. Holcomb T, Moran M (1991) Local training for radial basis function networks: towards solving the hidden unit problem. In: The proceedings of the American control conference, pp 2331–2336

  122. Lee S, Rhce MK (1991) A Gaussian potential function network with hierarchically self-organizing learning. Neural Netw 4:207–224

    Article  Google Scholar 

  123. Musavi MT, Ahmed W, Chan KH, Faris KB, Hummels DM (1992) On the training of radial basis function classifiers. Neural Netw 5:595–603

    Article  Google Scholar 

  124. Lan Y, Soh YC, Huang G-B (2010) Constructive hidden nodes selection of extreme learning machine for regression. Neurocomputing 73:3191–3199

    Article  Google Scholar 

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Acknowledgments

This work is supported by Islamic Azad University-South Tehran Branch under a research project entitled as “Chaotic Synchronization with Application in Secure Communication Based on Optimized Linear and Nonlinear Controllers Using Evolutionary Algorithms”.

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Authors and Affiliations

  1. Department of Communication Engineering, Faculty of Engineering, Islamic Azad University, South Tehran Branch, P.O. Box: 11365-4435, Tehran, Iran

    Mansour Sheikhan

  2. Modeling and Optimization Research Center in Science and Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran

    Reza Shahnazi

  3. Department of Electronic Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran

    Sahar Garoucy

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  1. Mansour Sheikhan
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  2. Reza Shahnazi
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  3. Sahar Garoucy
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Correspondence to Mansour Sheikhan.

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Sheikhan, M., Shahnazi, R. & Garoucy, S. Synchronization of general chaotic systems using neural controllers with application to secure communication. Neural Comput & Applic 22, 361–373 (2013). https://doi.org/10.1007/s00521-011-0697-0

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