gradient and least squares methods discussed in this chapter, and a portion of the section on gain schedule construction in Chapter 7 relies on the reader knowing at least one method from this chapter. In other words this chapter is important since many adaptive control techniques depend on the use of an estimator moreover. the sections on neural networks and genetic algorithms in Chapter 8 depend on this chapter in the sense that if you understand this chapter and those sections, you will see how those techniques relate to the ones discussed here. Otherwise the remainder of the book can be completed without this chapter; however, this chapter will provide for a deeper understanding of many of the concepts to be presented in Chapters 6 and 7. For example, the learning mechanism for the fuzzy model reference learning controller(FMrLC)described in Chapter 6 can be viewed as an identification algorithm that is used to tune a fuzzy controller 3.2 Fitting functions to data We begin this section by precisely defining the function approximation problem, in which you seek to synthesize a function to approximate another function that is inherently represented via a finite number of input-output associations (i.e, we only know how the function maps a finite number of points in its domain to its range). Next, we show how the problem of how to construct nonlinear system identifiers and nonlinear estimators is a special case of the problem of how to performgradient and least squares methods discussed in this chapter, and a portion of the section on gain schedule construction in Chapter 7 relies on the reader knowing at least one method from this chapter. In other words, this chapter is important since many adaptive control techniques depend on the use of an estimator. Moreover, the sections on neural networks and genetic algorithms in Chapter 8 depend on this chapter in the sense that if you understand this chapter and those sections, you will see how those techniques relate to the ones discussed here. Otherwise, the remainder of the book can be completed without this chapter; however, this chapter will provide for a deeper understanding of many of the concepts to be presented in Chapters 6 and 7. For example, the learning mechanism for the fuzzy model reference learning controller (FMRLC) described in Chapter 6 can be viewed as an identification algorithm that is used to tune a fuzzy controller. 3.2 Fitting Functions to Data We begin this section by precisely defining the function approximation problem, in which you seek to synthesize a function to approximate another function that is inherently represented via a finite number of input-output associations (i.e., we only know how the function maps a finite number of points in its domain to its range). Next, we show how the problem of how to construct nonlinear system identifiers and nonlinear estimators is a special case of the problem of how to perform