Approximation of multi-variate functions by means of adaptive basis functions

In this thesis we want to give an overview about approximating functions with general radial basis functions (GRBF). After introducing the theory of function approximation and neural networks some constructive learning algorithms are discussed. The main attention is directed to the algorithm of Pietruschka/Kinder for which an extension is introduced which allows a free choise of basis functions. For the sake of showing how Fuzzy Logic and neural nets can be used at once we introduce a method for building a fuzzy system from input-output data. This method by Lin and Cunningham uses so-called fuzzy neural networks. After that we introduce the considerations about the right choice of basis function presented by Smagt and Groen. They also contribute their own algorithm to the topic of approximation. Finally we want to demonstrate the usage of concepts of GRBFs for path planning algorithms.