Fuzzy Logic, Identification and Predictive Control by Jairo Jose Espinosa Oviedo download in iPad, ePub, pdf
This chapter presents some of the methods used to construct fuzzy models that replicate the behavior of a given function. According to the tuned parameters and the strategies, different methods have been proposed in the literature.
In this part, this book presents an analytical study of the approxi- mation capabilities of the different types of membership functions. The theory itself has continued to develop as this excellent and insightful monograph by authors Jairo Espinosa, Joos Vandewalle and Vincert Wertz shows.
The method improves the generalization capabilities of the fuzzy models. It is illustrated by means of a graphical example. Among the Mamdani models the best model is the model generated us- ing Gaussian membership functions. The gradient descent method calculates parameters on the antecedents and the consequences of the fuzzy inference system. Then the problem is reduced to a robust quadratic program.
Another very interesting property of this interpolation is that it has a continuous derivative at the extremes. As shown in the previous sections, the shape and the distribution affect the smoothness and the accuracy of the approximation. Such a property is not present when triangular functions are used.
Different types of fuzzy models have been proposed in the literature. The chapter begins with the formulation of the prob- lem.
The chapter includes an analysis of the structure of the fuzzy models, which are more suitable to be applied in system identifi- cation. For this reason, these membership functions are not covered in this study.
The initial position of the membership functions is another element that must be chosen. Fuzzy models can be dynamic or static. The chapter then pays attention to methods based on direct synthesis, and the method of feedback linearization is proposed where the models used to lin- earize the affine system are fuzzy models. The chapter is completed with a list of possible ways to describe the uncertainty of the models. Applications have been made in such diverse areas as medicine, engineering, management, behavioral science, just to mention some.
The chapter begins by formulating the problem of system identifica- tion using fuzzy models. The series offers an opportu- nity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The parameters can be refined to improve the approximation by applying gradient descent. Gradient descent techniques, clustering and evolutionary techniques are explained in this chapter.