Janczak A. Identification of Nonlinear Systems Using Neural Networks and Polynomial Models. A Block-Oriented Approach

Springer, 2005. — 208 p.The identification of nonlinear systems using the block-oriented approach has been developed since the half of 1960s. A large amount of knowledge on this subject has been accumulated through literature. However, publications are scattered over many papers and there is no book which presents the subject in a unified framework. This has created an increasing need to systemize the existing identification methods and along with a presentation of some original results have been the main incentive to write this book. In writing the book, an attempt has been made at the presentation of some new ideas concerning the model parameter adjusting with gradient-based techniques.
Two types of models, considered in this book, use neural networks and polynomials as representations of Wiener and Hammerstein systems. The focus is placed on Wiener and Hammerstein models in which the nonlinear element is represented by a polynomial or a two-layer perceptron neural network with hyperbolic tangent hidden layer nodes and linear output nodes. Pulse transfer function models are common representations of system dynamics in both neural network and polynomial Wiener and Hammerstein models.
Neural network and polynomial models reveal different properties such as the approximation accuracy, computational complexity, available parameter and structure optimization methods, etc. All these differences make them complementary in solving many practical problems. For example, it is well known that the approximation of some nonlinear functions requires polynomials of a high order and this, in turn, results in a high parameter variance error. The approximation with neural network models is an interesting alternative in such cases.Neural network Wiener models
Neural network Hammerstein models
Polynomial Wiener models
Polynomial Hammerstein models
Applications