**6. Conclusion**

The fuzzy systems are a convenient and efficient alternative for solution of problems where the fuzzy statements are well defined. Nevertheless, the project of a fuzzy system may became difficult for large and complex systems, when the control quality depends of "tryand-error" methods for defining the best membership functions to solve the problem.

The meta-heuristic method training modulus provides an automatic way for the adjustment of the membership functions parameters. These techniques show that the performance of a fuzzy control may be improved through the genetic algorithms, the particle swarm optimization or the hybrid particle swarm optimization, substituting for the "try-and-error" method, as used before by students for this purpose, with no good results.

The meta-heuristic methods provided distinctive advantages for the optimization of membership functions, resulting in a global survey, reducing the chances of ending into a local minimum, once it uses several sets of simultaneous solutions. The fuzzy logic supplied the evaluation function, a stage of the meta-heuristic methods where the adjustment is settled.

### **7. Acknowledgment**

The authors would like to express their thanks to the financial support of this work given by the Brazilian research agencies: CNPq, CAPES, and FAPEMIG.

#### **8. References**

418 Fuzzy Inference System – Theory and Applications

Average 459.07 363.13 444,83 347,27

Table 6. Results of simulations for different initial position from the used to training

The fuzzy systems are a convenient and efficient alternative for solution of problems where the fuzzy statements are well defined. Nevertheless, the project of a fuzzy system may became difficult for large and complex systems, when the control quality depends of "tryand-error" methods for defining the best membership functions to solve the problem.

The meta-heuristic method training modulus provides an automatic way for the adjustment of the membership functions parameters. These techniques show that the performance of a fuzzy control may be improved through the genetic algorithms, the particle swarm

**Human Setting**

**Iterations generated by Fuzzy Controls** 

**GA Trained PSO Trained HPSO** 

**Trained** 

**Case X Y Car Angle**

**6. Conclusion** 


**System Identification Using Fuzzy Cerebellar** 

Being an artificial neural network inspired by the cerebellum, the cerebellar model articulation controller (CMAC) was firstly developed in (Albus, 1975a, 1975b). With the advantages such as fast learning speed, high convergence rate, good generalization capability, and easier hardware implementation (Lin & Lee, 2009; Peng & Lin, 2011), the CMAC has been successfully applied to many fields; for example, identification (Lee et al., 2004), image coding (Iiguni, 1996), ultrasonic motors (Leu et al., 2010), grey relational analysis (Chang et al., 2010), pattern recognition (Glanz et al., 1991), robot control (Harmon et al., 2005; Mese, 2003; Miller et al., 1990), signal processing (Kolcz & Allinson, 1994), and diagnosis (Hung & Wang, 2004; Wang & Jiang, 2004). However, there are three main drawbacks of Albus' CMAC, i.e., larger required computing memory (Lee et al., 2007; Leu et al., 2010; Lin et al., 2008)), relatively poor ability of function approximation (Commuri & Lewis, 1997; Guo et al., 2002; Ker et al., 1997), and difficulty of adaptively selecting

In order to tackle these disadvantages, several methods, such as online-based clustering (Kasabov & Song, 2002; Tung & Quek, 2002) for the above-mentioned first drawback, Bspline functions (Lane et al., 1992; Wu & Pratt, 1999) and fuzzy concepts (Jou, 1992; Chen, 2001; Guo et al., 2002; Ker et al., 1997; Lai & Wong, 2001; Zhang & Qian, 2000) for the second one, and competitive learning (Chow & Menozzi, 1994), clustering (Hwang & Lin, 1998) and Shannon's entropy and golden-section search (Lee et al., 2003) for the third one, were proposed. Among these approaches, further improvements were implemented by Lin et al.

The rest of this chapter is organized as follows. Starting from the first CMAC model in 1975 the development processes, related learning algorithms and system identification examples of the fuzzy CMACs are briefly reviewed in section 2. Sections 3 and 4 respectively discuss the self constructing FCMAC (SC-FCMAC) and the powerful parametric FCMAC (P-FCMAC). Lastly, section 5 concludes this chapter, with suggested directions of further

structural parameters (Hwang & Lin, 1998; Lee et al., 2003).

(2008) with self-constructing algorithm and Gaussian basis functions.

**1. Introduction** 

researches.

Corresponding Author

 \*

**Model Articulation Controllers** 

Cheng-Jian Lin\* and Chun-Cheng Peng *National Chin-Yi University of Technology* 

*Taiwan, R. O. C.* 

Ross, T.J. (2010). *Fuzzy Logic with Engineering Applications*, John Wiley and Sons, ISBN 9780470743768, West Sussex, United Kingdom. **20** 
