DocumentCode :
1400502
Title :
Complete memory structures for approximating nonlinear discrete-time mappings
Author :
Stiles, Bryan Waitsel ; Sandberg, Irwin W. ; Ghosh, Joydeep
Author_Institution :
Dept. of Electr. & Comput. Eng., Texas Univ., Austin, TX, USA
Volume :
8
Issue :
6
fYear :
1997
fDate :
11/1/1997 12:00:00 AM
Firstpage :
1397
Lastpage :
1409
Abstract :
This paper introduces a general structure that is capable of approximating input-output maps of nonlinear discrete-time systems. The structure is comprised of two stages, a dynamical stage followed by a memoryless nonlinear stage. A theorem is presented which gives a simple necessary and sufficient condition for a large set of structures of this form to be capable of modeling a wide class of nonlinear discrete time systems. In particular, we introduce the concept of a “complete memory”. A structure with a complete memory dynamical stage and a sufficiently powerful memoryless stage is shown to be capable of approximating arbitrarily wide class of continuous, causal, time invariant, approximately-finite-memory mappings between discrete-time signal spaces. Furthermore, we show that any bounded-input bounded output, time-invariant, causal memory structure has such an approximation capability if and only if it is a complete memory. Several examples of linear and nonlinear complete memories are presented. The proposed complete memory structure provides a template for designing a wide variety of artificial neural networks for nonlinear spatiotemporal processing
Keywords :
discrete time systems; encoding; feedforward neural nets; function approximation; multidimensional systems; multilayer perceptrons; nonlinear systems; RBF neural networks; approximation theory; complete memory structures; discrete-time systems; functional analysis; input-output maps; modeling; multidimensional systems; multilayer perceptrons; nonlinear systems; temporal encoding; Approximation methods; Artificial neural networks; Automata; Functional analysis; Multidimensional systems; Polynomials; Power system modeling; Signal mapping; Spatiotemporal phenomena; Sufficient conditions;
fLanguage :
English
Journal_Title :
Neural Networks, IEEE Transactions on
Publisher :
ieee
ISSN :
1045-9227
Type :
jour
DOI :
10.1109/72.641463
Filename :
641463
Link To Document :
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