Mathematical Problems in Engineering
Volume 6 (2000), Issue 1, Pages 61-83

Passivation and control of partially known SISO nonlinear systems via dynamic neural networks

J. Reyes-Reyes,1 W. Yu,1 and A. S. Poznyak1,2

1CINVESTAV-IPN, Automatic Control Department, A.P.14-740, Mexico D.F. CP 07360, Mexico
2Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence 66045, KS, USA

Received 13 September 1999; Revised 29 October 1999

Copyright © 2000 J. Reyes-Reyes et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN), containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both successful identification and passivation effects, is derived. Based on this adaptive DNN model, an adaptive feedback controller, serving for wide class of nonlinear systems with an a priori incomplete model description, is designed. Two typical examples illustrate the effectiveness of the suggested approach.