- Ferrari, Silvia and Stengel, Robert F., Smooth function approximation using neural networks,
IEEE Transactions on Neural Networks, vol. 16 no. 1
pp. 24 - 38 [TNN.2004.836233] .
(last updated on 2007/04/10)
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. © 2005 IEEE.
Functions;Approximation theory;Linear algebra;Nonlinear equations;Set theory;Algorithms;Recurrent neural networks;Feedback control;Control system synthesis;Linear control systems;