Lur´e systems with multilayer perceptron and recurrent neural networks: absolute stability and dissipativity

Author

Soykens, J.A.K. ; Vandewalle, J. ; De Moor, B.

Author_Institution

Dept. of Electr. Eng., Katholieke Univ., Leuven, Heverlee, Belgium

Volume

44

Issue

4

fYear

1999

fDate

4/1/1999 12:00:00 AM

Firstpage

770

Lastpage

774

Abstract

Sufficient conditions for absolute stability and dissipativity of continuous-time recurrent neural networks with two hidden layers are presented. In the autonomous case this is related to a Lur´e system with multilayer perceptron nonlinearity. Such models are obtained after parametrizing general nonlinear models and controllers by a multilayer perceptron with one hidden layer and representing the control scheme in standard plant form. The conditions are expressed as matrix inequalities and can be employed for nonlinear H_∞ control and imposing closed-loop stability in dynamic backpropagation

Keywords

H^∞ control; Lyapunov methods; absolute stability; backpropagation; closed loop systems; matrix algebra; multilayer perceptrons; neurocontrollers; nonlinear control systems; recurrent neural nets; H_∞ control; Lure systems; Lyapunov function; absolute stability; backpropagation; closed-loop systems; dissipativity; matrix inequality; multilayer perceptron; nonlinear control systems; recurrent neural networks; sufficient conditions; Backpropagation; Control systems; Linear matrix inequalities; Multilayer perceptrons; Neural networks; Nonlinear control systems; Nonlinear systems; Recurrent neural networks; Stability; Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.754815

Filename

754815