Validation of a particular class of dynamical systems

The aim of this paper is to study the validation of a model for non-linear systems. It evaluates the ability of a model to simulate the behavior of an unknown system (Σ). This is a central problem in identification ([2]). In almost cases, validation consists, by a statistical approach, in a test that falsifies or not falsifies the model, using a given discrete sampled data set. Our approach, based on combinatorial techniques, is different and provides: • an exact symbolic computation of the error E, due to the approximation of (Σ) by a family of bilinear systems described by generating series. This produces an estimation of E, that is essential in the measure of model’s quality [2]. Particularly, we can determine intervals where our model is “acceptable”, independently of the data set choosen for validation, as in discret case. • a computing tool parameterized by the input and the system’s behavior. In fact, our computation is a sum of differential monomials in the input functions and behavior system. So, we can determine and separate input and system contributions to this error and we obtain, in this way, a valuation process for rough and oscillating inputs as well as smooth inputs.