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Self-Organizing Recurrent Wavelet Fuzzy Neural Network-Based Control System Design for MIMO Uncertain Nonlinear Systems Using TOPSIS Method

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Abstract

The major objective of this study is to design an effective control algorithm for dealing with multiple-input–multiple-output uncertain nonlinear systems. Novelty advantages of the proposed method include: (1) The network has the maximum initial rules; it helps to increase the responsiveness of the system; (2) the network has two dynamic thresholds: One dynamic threshold is utilized to consider whether to retain or to delete the existing rules and the other is used for generating a new rule; (3) the fuzzy neural network-based system can automatically construct the network structure and adjust the parameters of the system; (4) the network uses multiple combination techniques, such as sliding mode control, adaptive control, recurrent unit, wavelet function, fuzzy logic, neural network, and technique for order of preference by similarity to ideal solution multi-criteria decision analysis method. Based on the advantages of the above techniques, a self-organizing recurrent wavelet fuzzy neural network control system is designed comprising a main controller and a robust compensator. The gradient descent method is used to online tune the parameters for the main controller, and a Lyapunov stability theorem is applied to guarantee the system’s stability. Finally, the proposed control system is applied to a nonlinear chaotic system, an inverted double-pendulum system, and an unmanned aerial vehicle motion control to verify the effectiveness of the proposed control scheme. The simulation results show that the proposed control scheme can achieve favorable control performance.

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References

  1. Zhang, H., Cui, Y., Wang, Y.: Hybrid fuzzy adaptive fault-tolerant control for a class of uncertain nonlinear systems with unmeasured states. IEEE Trans. Fuzzy Syst. 25(5), 1041–1050 (2017)

    Article  Google Scholar 

  2. Wu, L.-B., Yang, G.-H.: Adaptive output fuzzy fault accommodation for a class of uncertain nonlinear systems with multiple time delays. IEEE Trans. Fuzzy Syst. 26(2), 1052–1057 (2018)

    Article  MathSciNet  Google Scholar 

  3. Gao, Y.-F., Sun, X.-M., Wen, C., Wang, W.: Adaptive tracking control for a class of stochastic uncertain nonlinear systems with input saturation. IEEE Trans. Autom. Control 62, 2498–2504 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zouari, F., Boulkroune, A., Ibeas, A., Arefi, M.M.: Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation. Neural Comput. Appl. 28, 993–1010 (2017)

    Article  Google Scholar 

  5. Li, H., Wang, J., Lam, H.-K., Zhou, Q., Du, H.: Adaptive sliding mode control for interval type-2 fuzzy systems. IEEE Trans. Syst. Man Cybern. Syst. 46(12), 1654–1663 (2016)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  7. Wang, Y., **e, L., de Souza, C.E.: Robust control of a class of uncertain nonlinear systems. Syst. Control Lett. 19(2), 139–149 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, New York (1992)

    Book  MATH  Google Scholar 

  9. Wang, S.-Y., Liu, F.-Y., Chou, J.-H.: Adaptive TSK fuzzy sliding mode control design for switched reluctance motor DTC drive systems with torque sensorless strategy. Appl. Soft Comput. 66, 278–291 (2018)

    Article  Google Scholar 

  10. Wang, Y., Shen, H., Karimi, H.R., Duan, D.: Dissipativity-based fuzzy integral sliding mode control of continuous-time T–S fuzzy systems. IEEE Trans. Fuzzy Syst. (2017). https://doi.org/10.1109/TFUZZ.2017.2710952

    Google Scholar 

  11. Hung, J.Y., Gao, W., Hung, J.C.: Variable structure control: a survey. IEEE Trans. Ind. Electron. 40(1), 2–22 (1993)

    Article  Google Scholar 

  12. Tudoroiu, N., Elefterie, L., Tudoroiu, E.-R., Kecs, W., Dobritoiu, M., Ilias, N.: Real-time sliding mode observer estimator integration in hybrid electric vehicles battery management systems. In: Information Systems Architecture and Technology: Proceedings of 37th International Conference on Information Systems Architecture and Technology—ISAT 2016—Part III, pp. 15–28. Springer (2017)

  13. Phoemphon, S., So-In, C., Niyato, D.T.: A hybrid model using fuzzy logic and an extreme learning machine with vector particle swarm optimization for wireless sensor network localization. Appl. Soft Comput. 65, 101–120 (2018)

    Article  Google Scholar 

  14. Matuszek, C., Herbst, E., Zettlemoyer, L., Fox, D.: Learning to parse natural language commands to a robot control system. In: Experimental Robotics, pp. 403–415. Springer (2013)

  15. De Medeiros, T.H., Rocha, H.P., Torres, F.S., Takahashi, R.H.C., Braga, A.P.: Multi-objective decision in machine learning. J. Control Autom. Electr. Syst. 28(2), 217–227 (2017)

    Article  Google Scholar 

  16. Kim, J., Kim, H., Kang, P.: Keystroke dynamics-based user authentication using freely typed text based on user-adaptive feature extraction and novelty detection. Appl. Soft Comput. 62, 1077–1087 (2018)

    Article  Google Scholar 

  17. Hajek, P.: Predicting corporate investment/non-investment grade by using interval-valued fuzzy rule-based systems—a cross-region analysis. Appl. Soft Comput. 62, 73–85 (2018)

    Article  Google Scholar 

  18. Lin, D., Wang, X., Nian, F., Zhang, Y.: Dynamic fuzzy neural networks modeling and adaptive backstep** tracking control of uncertain chaotic systems. Neurocomputing 73(16), 2873–2881 (2010)

    Article  Google Scholar 

  19. Wang, Y., Lu, Z., Qu, Y., Li, L., Wang, N.: Improving prediction performance of GPS satellite clock bias based on wavelet neural network. GPS Solut. 21(2), 523–534 (2017)

    Article  Google Scholar 

  20. Capizzi, G., Sciuto, G.L., Napoli, C., Tramontana, E.: An advanced neural network based solution to enforce dispatch continuity in smart grids. Appl. Soft Comput. 62, 768–775 (2018)

    Article  Google Scholar 

  21. Wei, Y., Park, J.H., Qiu, J., Wu, L., Jung, H.Y.: Sliding mode control for semi-Markovian jump systems via output feedback. Automatica 81, 133–141 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ganesan, S., Ramesh, V., Umashankar, S., Sanjeevikumar, P.: Fuzzy-based microgrid energy management system using interleaved boost converter and three-level NPC inverter with improved grid voltage quality. In: Advances in Smart Grid and Renewable Energy. pp. 325–337. Springer (2018)

  23. Hafaifa, A., Laaouad, F., Laroussi, K.: A numerical structural approach to surge detection and isolation in compression systems using fuzzy logic controller. Int. J. Control Autom. Syst. 9(1), 69–79 (2011)

    Article  Google Scholar 

  24. Ullah, A.S., Noor-E-Alam, M.: Big data driven graphical information based fuzzy multi criteria decision making. Appl. Soft Comput. 63, 23–38 (2018)

    Article  Google Scholar 

  25. Wang, Y., Gao, Y., Karimi, H.R., Shen, H., Fang, Z.: Sliding mode control of fuzzy singularly perturbed systems with application to electric circuit. IEEE Trans. Syst. Man Cybern. Syst. (2017). https://doi.org/10.1109/TSMC.2017.2720968

    Google Scholar 

  26. Wei, Y., Qiu, J., Shi, P., Chadli, M.: Fixed-order piecewise-affine output feedback controller for fuzzy-affine-model-based nonlinear systems with time-varying delay. IEEE Trans. Circuits Syst. I Regul. Pap. 64(4), 945–958 (2017)

    Article  Google Scholar 

  27. Wang, Y., **a, 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)

    Article  MathSciNet  MATH  Google Scholar 

  28. Lin, C.-M., Le, T.-L.: PSO-self-organizing interval type-2 fuzzy neural network for antilock braking systems. Int. J. Fuzzy Syst. 19(5), 1362–1374 (2017)

    Article  MathSciNet  Google Scholar 

  29. Wei, Y., Qiu, J., Karimi, H.R.: Fuzzy-affine-model-based memory filter design of nonlinear systems with time-varying delay. IEEE Trans. Fuzzy Syst. 26(2), 504–517 (2018)

    Article  Google Scholar 

  30. Macnab, C.: Modifying CMAC adaptive control with weight smoothing in order to avoid overlearning and bursting. Neural Comput. Appl. (2017). https://doi.org/10.1007/s00521-017-3182-6

    Google Scholar 

  31. 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)

    Article  MathSciNet  Google Scholar 

  32. Liu, T., Deng, Y., Chan, F.: Evidential supplier selection based on DEMATEL and game theory. Int. J. Fuzzy Syst. 20(4), 1321–1333 (2018)

    Article  Google Scholar 

  33. Hwang, C.L., Yoon, K.: Multiple Attribute Decision Making: Methods and Applications: A State-of-The-Art Survey. Springer, Berlin (1981)

    MATH  Google Scholar 

  34. Estay-Ossandon, C., Mena-Nieto, A., Harsch, N.: Using a fuzzy TOPSIS-based scenario analysis to improve municipal solid waste planning and forecasting: a case study of Canary archipelago (1999–2030). J. Clean. Prod. 176, 1198–1212 (2018)

    Article  Google Scholar 

  35. Liu, L., Liu, X., Pei, J., Fan, W., Pardalos, P.M.: A study on decision making of cutting stock with frustum of cone bars. Oper. Res. Int. J. 17(1), 187–204 (2017)

    Article  Google Scholar 

  36. Afsordegan, A., Sánchez, M., Agell, N., Zahedi, S., Cremades, L.V.: Decision making under uncertainty using a qualitative TOPSIS method for selecting sustainable energy alternatives. Int. J. Environ. Sci. Technol. 13(6), 1419–1432 (2016)

    Article  Google Scholar 

  37. İç, Y.T.: A TOPSIS based design of experiment approach to assess company ranking. Appl. Math. Comput. 227(Supplement C), 630–647 (2014)

    MathSciNet  MATH  Google Scholar 

  38. Margain, L., Ochoa, A., Castillo, O., González, S., Gutiérrez, G.: Fuzzy TOPSIS method associated with improved selection of machines of high productivity. In: Distributed Computing and Artificial Intelligence, 13th International Conference, pp. 3–12. Springer (2016)

  39. Liu, J., Wei, Q.: Risk evaluation of electric vehicle charging infrastructure public-private partnership projects in China using fuzzy TOPSIS. J. Clean. Prod. 189, 211–222 (2018)

    Article  Google Scholar 

  40. 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. (2018). https://doi.org/10.1007/s40815-018-0482-7

    MathSciNet  Google Scholar 

  41. Rao, R.V.: Decision Making in The Manufacturing Environment: Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods. Springer, London (2007)

    MATH  Google Scholar 

  42. Lee, L.-W., Li, I.-H.: Design and implementation of a robust FNN-based adaptive sliding-mode controller for pneumatic actuator systems. J. Mech. Sci. Technol. 30(1), 381–396 (2016)

    Article  Google Scholar 

  43. Huang, X., Yan, Y., Zhou, Y.: Neural network-based adaptive second order sliding mode control of Lorentz-augmented spacecraft formation. Neurocomputing 222, 191–203 (2017)

    Article  Google Scholar 

  44. Ma, X., Sun, F., Li, H., He, B.: Neural-network-based sliding-mode control for multiple rigid-body attitude tracking with inertial information completely unknown. Inf. Sci. 400–401, 91–104 (2017)

    Article  Google Scholar 

  45. Lin, F.-J., Chen, S.-G., Sun, I.-F.: Intelligent sliding-mode position control using recurrent wavelet fuzzy neural network for electrical power steering system. Int. J. Fuzzy Syst. 19(5), 1344–1361 (2017)

    Article  MathSciNet  Google Scholar 

  46. 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)

    Article  Google Scholar 

  47. Wang, X., Jiang, R., Li, L., Lin, Y., Zheng, X., Wang, F.Y.: Capturing car-following behaviors by deep learning. IEEE Trans. Intell. Transp. Syst. 99, 1–11 (2017). https://doi.org/10.1109/TITS.2017.2706963

    Google Scholar 

  48. El-Sousy, F.F., Abuhasel, K.A.: Self-organizing recurrent fuzzy wavelet neural network-based mixed H 2/H ∞ adaptive tracking control for uncertain two-axis motion control system. IEEE Trans. Ind. Appl. 52(6), 5139–5155 (2016)

    Article  Google Scholar 

  49. Wei, Y., Park, J.H., Karimi, H.R., Tian, Y.-C., Jung, H.: Improved stability and stabilization results for stochastic synchronization of continuous-time semi-Markovian jump neural networks with time-varying delay. IEEE Trans. Neural Netw. Learn. Syst. 29(6), 2488–2501 (2018)

    Article  MathSciNet  Google Scholar 

  50. Shannon, C.E.: A mathematical theory of communication. Mob. Comput. Commun. Rev. 5(1), 3–55 (2001)

    Article  MathSciNet  Google Scholar 

  51. Zeleny, M.: Multiple Criteria Decision Making. McGraw-Hill, New York (1982)

    MATH  Google Scholar 

  52. Yu, Y., Zhang, S.: Adaptive backstep** synchronization of uncertain chaotic system. Chaos Solitons Fractals 21(3), 643–649 (2004)

    Article  MATH  Google Scholar 

  53. Lin, C.-M., Li, H.-Y.: Self-organizing adaptive wavelet CMAC backstep** control system design for nonlinear chaotic systems. Nonlinear Anal. Real World Appl. 14(1), 206–223 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  54. Kurfess, T.R.: Robotics and Automation Handbook. CRC Press, Boca Raton (2004)

    Book  Google Scholar 

  55. Zhou, S., Feng, G., Feng, C.-B.: Robust control for a class of uncertain nonlinear systems: adaptive fuzzy approach based on backstep**. Fuzzy Sets Syst. 151(1), 1–20 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  56. Lin, C.-M., Lin, H.Y.: TSK fuzzy CMAC-based robust adaptive backstep** control for uncertain nonlinear systems. IEEE Trans. Fuzzy Syst. 20(6), 1147–1154 (2012)

    Article  Google Scholar 

  57. Lin, C.-M., Tai, C.-F., Chung, C.-C.: Intelligent control system design for UAV using a recurrent wavelet neural network. Neural Comput. Appl. 24(2), 487–496 (2014)

    Article  Google Scholar 

  58. McLean, D.: Automatic Flight Control Systems. Prentice Hall, Englewood Cliffs (1990)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Yuan Ze University, Taoyüan, Taiwan, ROC

    Tuan-Tu Huynh, Tien-Loc Le & Chih-Min Lin

  2. Department of Electrical Electronic and Mechanical Engineering, Lac Hong University, Bien Hoa, Dong Nai, Vietnam

    Tuan-Tu Huynh & Tien-Loc Le

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  1. Tuan-Tu Huynh
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  2. Tien-Loc Le
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Correspondence to Chih-Min Lin.

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Huynh, TT., Le, TL. & Lin, CM. 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 (2019). https://doi.org/10.1007/s40815-018-0550-z

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