Smooth function approximation using neural networks.


Journal Article

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

Full Text

Duke Authors

Cited Authors

  • Ferrari, S; Stengel, RF

Published Date

  • January 2005

Published In

Volume / Issue

  • 16 / 1

Start / End Page

  • 24 - 38

PubMed ID

  • 15732387

Pubmed Central ID

  • 15732387

Electronic International Standard Serial Number (EISSN)

  • 1941-0093

International Standard Serial Number (ISSN)

  • 1045-9227

Digital Object Identifier (DOI)

  • 10.1109/tnn.2004.836233


  • eng