Global asymptotic convergence of nonlinear relaxation equations realised through a recurrent perceptron

Authors:
D. P. Mandic;J. A. Chambers
Affiliations:
Dept. of Electr. & Electron. Eng., Imperial Coll. of Sci., Technol. & Med., London, UK;-
Venue:
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 02
Year:
1999

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Abstract

Conditions for global asymptotic stability (GAS) of a nonlinear relaxation equation realised by a nonlinear autoregressive moving average (NARMA) recurrent perceptron are provided. Convergence is derived through fixed point iteration (FPI) techniques, based upon a contraction mapping feature of a nonlinear activation function of a neuron. Furthermore, nesting is shown to be a spatial interpretation of an FPI, which underpins a pipelined recurrent neural network (PRNN) for nonlinear signal processing.