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Interval type-2 fuzzy brain emotional control design for the synchronization of 4D nonlinear hyperchaotic systems

Abstract

This research provides a novel intelligent control structure for 4D nonlinear hyperchaotic systems. This is a hybrid design containing a new interval type-2 fuzzy fourfold function-link brain emotional controller and a smooth robust controller. It comprises a fuzzy inference system and three subnetworks. The subnetworks are a new fourfold function-link network, a type-2 fuzzy amygdala network and a type-2 fuzzy prefrontal cortex network that decrease the synchronization errors efficiently, follow the reference signal well, and achieve good performance. Two Lyapunov stability functions are utilized to get the adaptive laws, and they are applied to online tune the parameters of the system. The proposed design is used to synchronize two 4D nonlinear hyperchaotic systems and the simulation results are given to demonstrate its superiority and effectiveness.

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References

  1. Adeli H, Jiang X (2008) Intelligent infrastructure: neural networks, wavelets, and chaos theory for intelligent transportation systems and smart structures. CRC Press, London

    Book  Google Scholar 

  2. Andrievsky B, Kudryashova EV, Kuznetsov NV, Kuznetsova OA, Mokaev TN (2018) Hidden nonlinear oscillations in aircraft stabilization system with restrictions at the actuator control. In AIP Conference Proceedings, 2018. vol 1. AIP Publishing, p 020004

  3. Beal A, Blakely J, Corron N, Dean R (2016) High frequency oscillators for chaotic radar. In Radar Sensor Technology XX, 2016. International Society for Optics and Photonics, p 98290H

  4. Boubellouta A, Zouari F, Boulkroune A (2019) Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities. Int J Gen Syst 48:211–234

    MathSciNet  Article  Google Scholar 

  5. Chen A, Lu J, Lü J, Yu S (2006) Generating hyperchaotic Lü attractor via state feedback control. Physica A 364:103–110

    Article  Google Scholar 

  6. 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. Neurocomput 74:2797–2812

    Article  Google Scholar 

  7. Chen L, Tang S, Li Q, Zhong S (2018) A new 4D hyperchaotic system with high complexity. Math Comput Simul 146:44–56

    MathSciNet  MATH  Article  Google Scholar 

  8. Dashti ZAS, Gholami M, Hajimani M (2017) Brain emotional learning based intelligent controller for velocity control of an electro hydraulic servo system. IOSR J Elec Electron Eng 12:29–35

    Article  Google Scholar 

  9. Ding Z, Qiu H, Yang R, Jiang C, Zhou M (2019) Interactive-control-model for Human-computer interactive system based on Petri nets. IEEE Trans Autom Sci Eng 16:1800–1813

    Article  Google Scholar 

  10. 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. Expert Syst Appl 36:11836–11843

    Article  Google Scholar 

  11. Hsu C-F, Su C-T, Lee T-T (2016) Chaos synchronization using brain-emotional-learning-based fuzzy control. In 2016 Joint 8th International Conference on Soft Computing and Intelligent Systems (SCIS) and 17th International Symposium on Advanced Intelligent Systems (ISIS), 2016, pp 811–816

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

    Article  Google Scholar 

  13. Huynh T-T, Lin C-M, Le T-L, Nguyen NP, Hong S-K, Chao F (2020a) 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

    Article  Google Scholar 

  14. Huynh T-T, Lin C-M, Le T-L, Vu V-P, Chao F (2020b) Self-organizing double function-link fuzzy brain emotional control system design for uncertain nonlinear systems. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2020.3036404

    Article  Google Scholar 

  15. Huynh T-T, Lin C-M, Pham T-TT, Cho H-Y, Le T-L (2019b) 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

    MathSciNet  MATH  Article  Google Scholar 

  16. Huynh TT, Lin CM (2019) 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

  17. Huynh TT, Lin CM, Le TL (2020) A double function-link function-based fuzzy brain emotional controller for synchronizing a 4D hyper-chaotic system. In 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC), 2020, pp 1961–1965

  18. Huynh T-T, Le T-L, Lin C-M (2020d) A TOPSIS multi-criteria decision method-based intelligent recurrent wavelet CMAC control system design for MIMO uncertain nonlinear systems. Neural Comput Appl 32:4025–4043

    Article  Google Scholar 

  19. Kong Y, Gao J, Xu Y, Pan Y, Wang J, Liu J (2019) Classification of autism spectrum disorder by combining brain connectivity and deep neural network classifier. Neurocomput 324:63–68

    Article  Google Scholar 

  20. Le T-L (2019) Fuzzy C-means clustering interval type-2 cerebellar model articulation neural network for medical data classification. IEEE Access 7:20967–20973

    Article  Google Scholar 

  21. Le T-L, Huynh T-T, Hong S-K (2020a) Self-organizing interval type-2 fuzzy asymmetric CMAC design to synchronize chaotic satellite systems using a modified grey wolf optimizer. IEEE Access 8:53697–53709

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Le T-L, Huynh T-T, Hong SK (2020b) A modified grey wolf optimizer for optimum parameters of multilayer type-2 asymmetric fuzzy controller. IEEE Access 8:121611–121629

    Article  Google Scholar 

  24. LeDoux J (1991) Emotion and the limbic system concept Concepts in neuroscience

  25. Lin C-M, Chung C-C (2015) Fuzzy brain emotional learning control system design for nonlinear systems. Int J Fuzzy Syst 17:117–128

    MathSciNet  Article  Google Scholar 

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

    MathSciNet  Article  Google Scholar 

  27. Lin C-M, Huynh T-T (2019) Dynamic TOPSIS fuzzy cerebellar model articulation controller for magnetic levitation system. J Intell Fuzzy Syst 36:2465–2480

    Article  Google Scholar 

  28. Lin C-M, Huynh T-T, Le T-L (2018) Adaptive TOPSIS fuzzy CMAC back-stepping control system design for nonlinear systems. Soft Comput 23:6947–6966

    Article  Google Scholar 

  29. Lin C-M, Nguyen HB, Huynh T-T (2021a) A new self-organizing double function-link brain emotional learning controller for MIMO nonlinear systems using sliding surface. IEEE Access 9:73826–73842

    Article  Google Scholar 

  30. Lin C-M, Pham DH, Huynh T-T (2021b) Synchronization of chaotic system using a brain-imitated neural network controller and its applications for secure communications. IEEE Access 9:75923–75944

    Article  Google Scholar 

  31. Marzbanrad J, Babalooei M (2016) Grazing Bifurcations and Chaos of a Hydraulic Engine Mount International Journal of. Automot Eng 6:2182–2190

    Google Scholar 

  32. Mendel JM, Chimatapu R, Hagras H (2020) Comparing the performance potentials of singleton and non-singleton type-1 and interval type-2 fuzzy systems in terms of sculpting the state space. IEEE Trans Fuzzy Syst 28:783–794

    Article  Google Scholar 

  33. Mendel JM (2011) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice Hall, Upper Saddle River

    MATH  Google Scholar 

  34. Ni P, Xia Y, Li J, Hao H (2019) Using polynomial chaos expansion for uncertainty and sensitivity analysis of bridge structures. Mech Syst Signal Process 119:293–311

    Article  Google Scholar 

  35. Panahi S, Pham V-T, Rajagopal K, Boubaker O, Jafari S (2019) A new four-dimensional chaotic system with no equilibrium point. In recent advances in chaotic systems and synchronization. Elsevier, pp 63–76

  36. Patra JC, Pal RN (1995) A functional link artificial neural network for adaptive channel equalization. Signal Process 43:181–195

    MATH  Article  Google Scholar 

  37. Pham V-T, Kingni ST, Volos C, Jafari S, Kapitaniak T (2017) A simple three-dimensional fractional-order chaotic system without equilibrium: Dynamics, circuitry implementation, chaos control and synchronization. AEU-Int J Electron Commun 78:220–227

    Article  Google Scholar 

  38. Rahmani M, Ghanbari A, Ettefagh MM (2018) A novel adaptive neural network integral sliding-mode control of a biped robot using bat algorithm. J Vib Control 24:2045–2060

    MathSciNet  Article  Google Scholar 

  39. Rakheja P, Vig R, Singh P (2019) Optical asymmetric watermarking using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain. Optik 176:425–437

    Article  Google Scholar 

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

    Article  Google Scholar 

  41. Rong N, Wang Z, Ding S, Zhang H (2018) Interval type-2 regional switching T-S fuzzy control for time-delay systems via membership function dependent approach. Fuzzy Sets Syst 374:152–169

    MathSciNet  MATH  Article  Google Scholar 

  42. Sambas A, He S, Liu H, Vaidyanathan S, Hidayat Y, Saputra J (2020) Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system. Adv Difference Equ 2020:1–12

    MathSciNet  Article  Google Scholar 

  43. Sambas A, Mamat M, Arafa AA, Mahmoud GM, Mohamed MA, Sanjaya W (2019a) A new chaotic system with line of equilibria: dynamics, passive control and circuit design. Int J Electric Comput Eng 9:2088–8708

    Google Scholar 

  44. Sambas A, Mamat M, Viadyanathan S, Mohamed MA, Sanjaya WM (2018) A new 4-D chaotic system with hidden attractor and its circuit implementation. Int J Eng Technol 7:1245–1250

    Article  Google Scholar 

  45. Sambas A, Vaidyanathan S, Zhang S, Mohamed MA, Zeng Y, Azar AT (2021) A new 4-D chaotic hyperjerk system with coexisting attractors, its active backstepping control, and circuit realization. In Backstepping Control of Nonlinear Dynamical Systems. Elsevier, pp 73–94

  46. Sambas A, Vaidyanathan S, Zhang S, Putra WT, Mamat M, Mohamed MA (2019b) Multistability in a novel chaotic system with perpendicular lines of equilibrium: analysis, adaptive synchronization and circuit design. Engineering Letters 27

  47. Slotine JJE, Li W (1991) Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  48. Sothmann B, Sánchez R, Jordan AN, Büttiker M (2012) Rectification of thermal fluctuations in a chaotic cavity heat engine. Phys Rev B 85:205301

    Article  Google Scholar 

  49. Sun J, Shen Y, Yin Q, Xu C (2013) Compound synchronization of four memristor chaotic oscillator systems and secure communication Chaos: An Interdisciplinary. J Nonlinear Sci 23:013140

    MATH  Google Scholar 

  50. Vaidyanathan S, Dolvis LG, Jacques K, Lien C-H, Sambas A (2019) A new five-dimensional four-wing hyperchaotic system with hidden attractor, its electronic circuit realisation and synchronisation via integral sliding mode control. Int J Model Ident Control 32:30–45

    Article  Google Scholar 

  51. Vaidyanathan S, Pham V-T, Volos C, Sambas A (2018) A novel 4-D hyperchaotic Rikitake Dynamo system with hidden attractor, its properties, synchronization and circuit design. In: Pham V-T, Vaidyanathan S, Volos C, Kapitaniak T (eds) Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors. Springer, Cham, pp 345–364

    Chapter  Google Scholar 

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

    MATH  Article  Google Scholar 

  53. Wang H, Luo C, Wang X (2019a) 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

    Article  Google Scholar 

  54. Wang X, Kingni ST, Volos C, Pham VT, Vo HD, Jafari S (2019b) A fractional system with five terms: analysis, circuit, chaos control and synchronization. Int J Electron 106:109–120

    Article  Google Scholar 

  55. Wang Y, Shen H, Karimi HR, Duan D (2018) Dissipativity-based fuzzy integral sliding mode control of continuous-time TS fuzzy systems. IEEE Trans Fuzzy Syst 26:1164–1176

    Article  Google Scholar 

  56. Wu J, Liao X, Yang B (2017) Color image encryption based on chaotic systems and elliptic curve ElGamal scheme. Signal Process 141:109–124

    Article  Google Scholar 

  57. Xue W, Zhang M, Liu S, Li Y, Cang S (2019) Mechanical analysis and ultimate boundary estimation of the chaotic permanent magnet synchronous motor. J Franklin Inst 356:5378–5394

    MathSciNet  MATH  Article  Google Scholar 

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

    Article  Google Scholar 

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

    MathSciNet  Article  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 109-2811-E-155-504-MY3.

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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. Interval type-2 fuzzy brain emotional control design for the synchronization of 4D nonlinear hyperchaotic systems. Soft Comput 25, 14509–14535 (2021). https://doi.org/10.1007/s00500-021-06197-z

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Keywords

  • Interval type-2 fuzzy system
  • Fourfold function-link network
  • Fuzzy brain emotional controller
  • 4D nonlinear hyperchaotic system