Set Membership Estimation of Nonlinear Regressions

In this paper we propose a method, based on a Set Membership approach, for the estimation of nonlinear regressions models. At the contrary of most of the existing identi...cation approaches, the method presented in this paper does not need any assumption about the functional form of the model to be identi...ed, but uses only some prior information on its regularity and on the size of noise corrupting the measurements. The aim is to evaluate not only a nominal model but a model set, describing the inherent uncertainty of the regression function coming from ...nite and noise corrupted data. This is obtained by computing the optimal bounds on the regression function , i.e. its tightest lower and upper bounds compatible with measured data and with the given assumptions on the regression function and on noise. Moreover, necessary and su¢cient conditions are given for validating the prior assumptions. The e¤ectiveness of the method is tested on a water heater identi...cation problem, where the obtained models are compared in simulation with other nonlinear models obtained by neural networks, Just In Time and Fuzzy approaches.