Neural, Fuzzy, and ApproximationBased Control
Tarıq Samad · 2009
The assumption of linearity must be given due credit for the tremendous practical impact that control systems have had over the last several decades. However, as the original challenges have been encountered and overcome, and as the control and automation of complex, large-scale problems are being sought, effective methods for dealing with nonlinear systems have become essential.One key component of nonlinear controls technology is representations or models of nonlinear systems that are derived from operational data. Such models, referred to asapproximators, are the focus of this chapter. Specific attention is paid to neural networks and fuzzy models. These topics are discussed within a general formulation that emphasizes their close relationships with other approximator structures. In this chapter, several associated properties are noted and defined, including universal approximation, linear and nonlinear parameterizations, generalization, and approximator transparency. Compared to most other chapters in this volume, this one is relatively theoretical. Less formal introductions to neural networks and fuzzy logic can be found in Chapter 5; some applications are discussed therein and in Chapter 16.An important problem in approximator development is the estimation of the approximator parameters. This chapter discusses some algorithms - specifically steepest descent, least-squares, and Lyapunov-based algorithms - that can be used for this purpose. Some degree of modeling error is inescapable, and this realization has motivated the development of extensions to parameter estimation algorithms.Readers interested in additional nonlinear control methods may also find Chapter 8 of interest, which provides a readable technical introduction to a popular nonlinear control design technique, slidingmode control.