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.

J. Reyes-Reyes, W. Yu, A. S. Poznyak.
Passivation and control of partially known SISO nonlinear systems via dynamic neural networks,
Mathematical Problems in Engineering,
DOI: 10.1155/S1024123X00001253