International Journal of Fuzzy Systems

, Volume 20, Issue 6, pp 1839–1856 | Cite as

Function-Link Fuzzy Cerebellar Model Articulation Controller Design for Nonlinear Chaotic Systems Using TOPSIS Multiple Attribute Decision-Making Method

  • Chih-Min Lin
  • Tuan-Tu Huynh


This paper aims to propose a more efficient control algorithm to select suitable firing nodes, improve the computational efficiency, reduce the number of firing rules and achieve good performance for nonlinear chaotic systems. A novel function-link fuzzy cerebellar model articulation controller (FLFCMAC) is designed by using a multiple attribute decision-making method named as technique for order of preference by similarity to ideal solution (TOPSIS). The TOPSIS is used to determine the optimal threshold values for receptive-field basis function in association memory space such that the firing fuzzy rules can be effectively reduced. In the TOPSIS design, the Shannon entropy index is used to derive the objective weights of the evaluation attribute. The proposed control system is composed of a TOPSIS-based FLCMAC (TFLFCMAC) and a fuzzy compensator. The TFLFCMAC is the main tracking controller employed to mimic an ideal controller, and the fuzzy compensator can eliminate the approximation error between the TFLFCMAC and the ideal controller. The parameters of the proposed TFLFCMAC are tuned online using the adaptation laws that are derived from a Lyapunov stability theorem, so that the system’s stability is guaranteed. Finally, the proposed control system is applied to a Duffing–Holmes chaotic system and a gyro chaotic system to illustrate its favorable control performance and to show its superiority to the other control techniques.


Technique for order of preference by similarity to ideal solution (TOPSIS) Entropy Fuzzy inference system Function-link (FL) Cerebellar model articulation controller (CMAC) Nonlinear chaotic system 



This paper was supported in part by the National Science Council of the Republic of China under Grand NSC 101-2221-E-155-026-MY3.

Compliance with Ethical Standards

Conflicts of interest

The authors declare that they have no conflicts of interest.


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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringYuan Ze UniversityZhongliTaiwan, ROC
  2. 2.Department of Electrical Electronic and Mechanical EngineeringLac Hong UniversityBien HoaVietnam

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