Approximate models for nonlinear dynamical systems and their generalization properties

In this paper, a methodology to obtain approximate models from input-output data for nonlinear, causal, time invariant discrete systems having a certain type of continuity condition called fading memory is presented. The region or domain of the input space, where the model can be applicable, is studied, as well as the importance of this study in applications as data processing and the qualification of the model quality. The structure is synthesized using a finite set of discrete Kautz systems, followed by a single hidden layer perceptron. The number of the Kautz systems is evaluated by Lipschitz quotients, while the number of hidden neurons is bounded using a pruning technique. Examples illustrating the proposed methodology are presented.