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Wavelet Interval Type-2 Fuzzy Quad-Function-Link Brain Emotional Control Algorithm for the Synchronization of 3D Nonlinear Chaotic Systems

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Abstract

This study provides a novel quad-function-link network to adjust the lower and upper weights of a wavelet interval type-2 fuzzy brain emotional structure to increase the response and performance for the synchronization of 3D nonlinear chaotic systems. The proposed control system is a hybrid method that comprises a new wavelet interval type-2 fuzzy quad-function-link brain emotional controller and a robust controller. It contains a fuzzy inference system and three substructures with five layers. The substructures are an amygdala, a prefrontal cortex, and a novel quad-function-link network that can adjust the weights efficiently for the amygdala and prefrontal cortex networks to achieve the synchronization of the master–slave systems well with reduced tracking errors. Then, a Lyapunov stability function is employed to provide the adaptive laws, and they are effectively used online to adjust the system parameters. Finally, simulation studies of two 3D nonlinear chaotic systems are used to verify the superiority and advantage of the proposed algorithm.

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References

  1. Boccaletti, S., Kurths, J., Osipov, G., Valladares, D., Zhou, C.: The synchronization of chaotic systems. Phys. Rep. 366(1–2), 1–101 (2002)

    MathSciNet  MATH  Google Scholar 

  2. Selvam A.M., Nonlinear dynamics and chaos: applications in meteorology and atmospheric physics. In: Self-organized Criticality and Predictability in Atmospheric Flows. Springer Atmospheric Sciences. Springer, Cham, 2017

  3. Yau, H.T., Wu, S.Y., Chen, C.L., Li, Y.C.: Fractional-order chaotic self-synchronization-based tracking faults diagnosis of ball bearing systems. IEEE Trans. Ind. Electron. 63(6), 3824–3833 (2016)

    Google Scholar 

  4. Wang, H., Luo, C., Wang, X.: Synchronization and identification of nonlinear systems by using a novel self-evolving interval type-2 fuzzy LSTM-neural network. Eng. Appl. Artif. Intell. 81, 79–93 (2019)

    Google Scholar 

  5. Ravi, V., Pradeepkumar, D., Deb, K.: Financial time series prediction using hybrids of chaos theory, multi-layer perceptron and multi-objective evolutionary algorithms. Swarm Evol. Comput. 36, 136–149 (2017)

    Google Scholar 

  6. Uversky, V.N.: Dancing protein clouds: the strange biology and chaotic physics of intrinsically disordered proteins. J. Biol. Chem. 291(13), 6681–6688 (2016)

    Google Scholar 

  7. Al Hasani, M.H., Al Naimee, K.A.: Impact security enhancement in chaotic quantum cryptography. Opt. Laser Technol. 119, 105575–105581 (2019)

    Google Scholar 

  8. Li, Y., Li, C.: Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period. Neurocomputing 173, 1341–1347 (2016)

    Google Scholar 

  9. Martins, V., Rodrigues, A.C., Cerdeira, H., Machado, B.S.: Phase-lag synchronization analysis in complex systems with directed inter-relations. Eur. Phys. J. Spec. Topics 225(1), 41–49 (2016)

    Google Scholar 

  10. Gasri, A., Ouannas, A., Ojo, K.S., Pham, V.-T.: Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems. Nonlinear Anal. Modell. Control 23(4), 583–598 (2018)

    MathSciNet  MATH  Google Scholar 

  11. Berber, S.M.: Discrete time domain analysis of chaos-based wireless communication systems with imperfect sequence synchronization. Signal Process. 154, 198–206 (2019)

    Google Scholar 

  12. Akgul, A., Calgan, H., Koyuncu, I., Pehlivan, I., Istanbullu, A.: Chaos-based engineering applications with a 3D chaotic system without equilibrium points. Nonlinear Dyn. 84(2), 481–495 (2016)

    MathSciNet  Google Scholar 

  13. Wang, X., Kingni, S.T., Volos, V., Pham, V.T., Vo Hoang, D., Jafari, S.: A fractional system with five terms: analysis, circuit, chaos control and synchronization. Int. J. Electron. 106(1), 109–120 (2019)

    Google Scholar 

  14. He, S., Sun, K., Wang, H.: Dynamics and synchronization of conformable fractional-order hyperchaotic systems using the Homotopy analysis method. Commun. Nonlinear Sci. Numer. Simul. 73, 146–164 (2019)

    MathSciNet  MATH  Google Scholar 

  15. Xu, Y., Li, Q., Li, W.: Periodically intermittent discrete observation control for synchronization of fractional-order coupled systems. Commun. Nonlinear Sci. Numer. Simul. 74, 219–235 (2019)

    MathSciNet  MATH  Google Scholar 

  16. Kocamaz, U.E., Cevher, B., Uyaroğlu, Y.: Control and synchronization of chaos with sliding mode control based on cubic reaching rule. Chaos Solitons Fractals 105, 92–98 (2017)

    MathSciNet  MATH  Google Scholar 

  17. Han, M., Zhong, K., Qiu, T., Han, B.: Interval type-2 fuzzy neural networks for chaotic time series prediction: a concise overview. IEEE Trans. Cybern. 49(7), 2720–2731 (2019)

    Google Scholar 

  18. Akbarzadeh-T, M.-R., Hosseini, S., Naghibi-Sistani, M.-B.: Stable indirect adaptive interval type-2 fuzzy sliding-based control and synchronization of two different chaotic systems. Appl. Soft Comput. 55, 576–587 (2017)

    Google Scholar 

  19. Tai, W., Teng, Q., Zhou, Y., Zhou, J., Wang, Z.: Chaos synchronization of stochastic reaction-diffusion time-delay neural networks via non-fragile output-feedback control. Appl. Math. Comput. 354, 115–127 (2019)

    MathSciNet  MATH  Google Scholar 

  20. Huynh, T.T., Le, T.L., Lin, C.M.: Self-organizing recurrent wavelet fuzzy neural network-based control system design for mimo uncertain nonlinear systems using topsis method. Int. J. Fuzzy Syst. 21(2), 468–487 (2019)

    Google Scholar 

  21. H. Y. Li, C. M. Lin, C. H. Lee, J. G. Juang: Adaptive function-link fuzzy CMAC control system design for MIMO nonlinear chaotic systems. Int. J. Fuzzy Syst. 16(4), 2014

  22. Huynh, T.T., Lin, C.M., Pham, T.T.T., Cho, H.Y., Le, T.L.: A modified function-link fuzzy cerebellar model articulation controller using a PI-type learning algorithm for nonlinear system synchronization and control. Chaos Solitons Fractals 118, 65–82 (2019)

    MathSciNet  MATH  Google Scholar 

  23. Zhou, Q., Chao, F., Lin, C.M.: A functional-link-based fuzzy brain emotional learning network for breast tumor classification and chaotic system synchronization. Int. J. Fuzzy Syst. 20(2), 349–365 (2018)

    MathSciNet  Google Scholar 

  24. Le, T.L., Lin, C.M., Huynh, T.T.: Self-evolving type-2 fuzzy brain emotional learning control design for chaotic systems using PSO. Appl. Soft Comput. 73, 418–433 (2018)

    Google Scholar 

  25. Zhang, B., Deng, F., Zhao, X., Zhang, B.: Hybrid control of stochastic chaotic system based on memristive Lorenz system with discrete and distributed time-varying delays. IET Control Theory Appl. 10(13), 1513–1523 (2016)

    MathSciNet  Google Scholar 

  26. Li, H.L., Cao, J., Hu, C., Zhang, L., Wang, Z.: Global synchronization between two fractional-order complex networks with non-delayed and delayed coupling via hybrid impulsive control. Neurocomputing 356, 31–39 (2019)

    Google Scholar 

  27. LeDoux, J.: Emotion and the limbic system concept. Concepts Neurosci. 2, 169–199 (1991)

    Google Scholar 

  28. Rouhani, H., Jalili, M., Araabi, B.N., Eppler, W., Lucas, C.: Brain emotional learning based intelligent controller applied to neurofuzzy model of micro-heat exchanger. Expert Syst. Appl. 32(3), 911–918 (2007)

    Google Scholar 

  29. Fang, W., Chao, F., Lin, C.-M., Yang, L., Shang, C., Zhou, C.: An improved fuzzy brain emotional learning model network controller for humanoid robots. Front. Neurorobot. 13, 2 (2019)

    Google Scholar 

  30. Wu, Q., Lin, C.M., Fang, W., Chao, F., Yang, L., Shang, C., Zhou, C.: Self-organizing brain emotional learning controller network for intelligent control system of mobile robots. IEEE Access 6, 59096–59108 (2018)

    Google Scholar 

  31. Zhao, J., Lin, C.M., Chao, F.: Wavelet fuzzy brain emotional learning control system design for mimo uncertain nonlinear systems. Front. Neurosci. (2019). https://doi.org/10.3389/fnins.2018.00918

    Article  Google Scholar 

  32. Fakhrmoosavy, S.H., Setayeshi, S., Sharifi, A.: A modified brain emotional learning model for earthquake magnitude and fear prediction. Eng. Comput. 34(2), 261–276 (2018)

    Google Scholar 

  33. Lin, C.-M., Le, T.L., Huynh, T.T.: Self-evolving function-link interval type-2 fuzzy neural network for nonlinear system identification and control. Neurocomputing 275, 2239–2250 (2018)

    Google Scholar 

  34. Vu, V.P., Wang, W.J.: Polynomial controller synthesis for uncertain large-scale polynomial ts fuzzy systems. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/tcyb.2019.2895233

    Article  Google Scholar 

  35. Wang, Y., Xia, Y., Shen, H., Zhou, P.: SMC design for robust stabilization of nonlinear markovian jump singular systems. IEEE Trans. Autom. Control 63(1), 219–224 (2018)

    MathSciNet  MATH  Google Scholar 

  36. Lin, C.M., Huynh, T.T., Le, T.L.: Adaptive TOPSIS fuzzy CMAC back-stepping control system design for nonlinear systems. Soft. Comput. 23(16), 6947–6966 (2019)

    Google Scholar 

  37. Zhao, J., Lin, C.M.: Wavelet-TSK-type fuzzy cerebellar model neural network for uncertain nonlinear systems. IEEE Trans. Fuzzy Syst. 27(3), 549–558 (2019)

    Google Scholar 

  38. Huynh, T.T., et al.: A new self-organizing fuzzy cerebellar model articulation controller for uncertain nonlinear systems using overlapped Gaussian membership functions. IEEE Trans. Ind. Electron. (2019). https://doi.org/10.1109/TIE.2019.2952790

    Article  Google Scholar 

  39. Macnab, C.J.B.: Using RBFs in a CMAC to prevent parameter drift in adaptive control. Neurocomputing 205, 45–52 (2016)

    Google Scholar 

  40. Lin, C.M., Chen, T.Y.: Self-organizing cmac control for a class of mimo uncertain nonlinear systems. IEEE Trans. Neural Networks 20(9), 1377–1384 (2009)

    Google Scholar 

  41. Hramov, A.E., Koronovskii, A.A., Makarov, V.A., Pavlov, A.N., Sitnikova, E.: Wavelets in Neuroscience. Springer, Berlin (2015)

    MATH  Google Scholar 

  42. Chui, C.K.: An Introduction to Wavelets. Elsevier, Amsterdam (2016)

    MATH  Google Scholar 

  43. Tang, J., Deng, C., Huang, G.-B.: Extreme learning machine for multilayer perceptron. IEEE Trans. Neur. Netw. Learn. Syst. 27(4), 809–821 (2015)

    MathSciNet  Google Scholar 

  44. Yang, J., Ma, J.: Feed-forward neural network training using sparse representation. Expert Syst. Appl. 116, 255–264 (2019)

    Google Scholar 

  45. Patra, J.C., Pal, R.N.: A functional link artificial neural network for adaptive channel equalization. Signal Process. 43(2), 181–195 (1995)

    MATH  Google Scholar 

  46. Lin, C.M., Huynh, T.T.: Function-link fuzzy cerebellar model articulation controller design for nonlinear chaotic systems using topsis multiple attribute decision-making method. Int. J. Fuzzy Syst. 20(6), 1839–1856 (2018)

    MathSciNet  Google Scholar 

  47. T. T. Huynh, C. M. Lin: Wavelet dual function-link fuzzy brain emotional learning system design for system identification and trajectory tracking of nonlinear systems, In 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC), 2019, pp. 1653–1657

  48. Yahyazadeh, M., Ranjbar Noei, A., Ghaderi, R.: Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control. ISA Trans. 50(2), 262–267 (2011)

    Google Scholar 

  49. Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice Hall, Upper Saddle River (2001)

    MATH  Google Scholar 

  50. Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  51. Park, J.H.: Adaptive synchronization of Rossler system with uncertain parameters. Chaos Solitons Fractals 25(2), 333–338 (2005)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors appreciate the financial support in part from the Ministry of Science and Technology of Republic of China under Grant MOST 106-2221-E-155-002-MY3.

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Authors and Affiliations

  1. Department of Electrical Engineering, Yuan Ze University, No. 135, Yuandong Road, Zhongli 320, Taoyuan, Taiwan, ROC

    Tuan-Tu Huynh & Chih-Min Lin

  2. Department of Electrical Electronic and Mechanical Engineering, Lac Hong University, No. 10, Huynh Van Nghe Road, Bien Hoa, Dong Nai, 760000, Vietnam

    Tuan-Tu Huynh & Tien-Loc Le

  3. Faculty of Mechanical and Aerospace Engineering, Sejong University, 143-747, Seoul, 05006, South Korea

    Tien-Loc Le, Ngoc Phi Nguyen & Sung-Kyung Hong

  4. Department of Cognitive Science, Xiamen University, Xiamen, China

    Fei Chao

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  1. Tuan-Tu Huynh
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Correspondence to Tuan-Tu Huynh or Chih-Min Lin.

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Huynh, TT., Lin, CM., Le, TL. et al. Wavelet Interval Type-2 Fuzzy Quad-Function-Link Brain Emotional Control Algorithm for the Synchronization of 3D Nonlinear Chaotic Systems. Int. J. Fuzzy Syst. 22, 2546–2564 (2020). https://doi.org/10.1007/s40815-020-00941-7

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