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Learning periodic signals with recurrent neural networks
Author(s) -
Weiss Martin G.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.199807815130
Subject(s) - artificial neural network , learning rule , trajectory , computer science , recurrent neural network , mode (computer interface) , control theory (sociology) , signal (programming language) , tracking (education) , artificial intelligence , mathematics , control (management) , physics , psychology , pedagogy , astronomy , programming language , operating system
We study a model for learning periodic signals in continouus time recurrent neural networks where the weight matrix has companion‐like structure. We use a model reference approach to derive a learning rule which solves the following learning problem: A network with unknown weights is running in closed loop mode giving a periodic trajectory. The output of this reference system is used as the input of a second learning network of the same structure with adjustable weights. We derive a learning rule (parameter adaptation law for the weights) which achieves the aims: Under appropriate assumptions the weights converge to the reference weights and the output tracking error goes to zero. If the learning dynamics is switched off after a sufficient period of time the learning system can approximately reproduce the reference signal when running in closed loop mode.