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

Author

Mandic, Danilo P. ; Chambers, Jonathon A.

Author_Institution

Dept. of Electr. & Electron. Eng., Imperial Coll. of Sci., Technol. & Med., London, UK

Volume

2

fYear

1999

fDate

15-19 Mar 1999

Firstpage

1037

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

Keywords

asymptotic stability; autoregressive moving average processes; fixed point arithmetic; iterative methods; nonlinear equations; numerical stability; perceptrons; recurrent neural nets; signal processing; FPI technique; GAS; NARMA; PRNN; contraction mapping feature; convergence; fixed point iteration; global asymptotic convergence; nonlinear activation function; nonlinear autoregressive moving average recurrent perceptron; nonlinear relaxation equations; nonlinear signal processing; pipelined recurrent neural network; recurrent perceptron; spatial interpretation; Asymptotic stability; Convergence; Linear systems; Logistics; Neurons; Nonlinear equations; Pipeline processing; Recurrent neural networks; Signal processing; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on

Conference_Location

Phoenix, AZ

ISSN

1520-6149

Print_ISBN

0-7803-5041-3

Type

conf

DOI

10.1109/ICASSP.1999.759885

Filename

759885