Equivalência de estruturas de modelos não lineares

Abstract

System identication aims to obtain mathematical models that describe the behavior of a dynamic system from measurements. A typical problem is to select a few models among many possibilities. The construction of nonlinear models, in particular the structure selection stage presents challenges for which there is no conclusive solutions. In view of practical limitations it is not always possible to nd the best model structure. It does not seem necessary or justiable to seek, in practical situations, a single best model structure. This work proposes a way to select from a pool of candidate structures, a subset of model structures that is consistent with the data. The solution proposed to solve this problem is a procedure based on Pareto sets and hypothesis testing to discriminate model structures. The result of the proposed method is a subset of model structures that is not distinguishable in terms of Pareto curves, for the used data, given a userdened condence level. As a byproduct, for each representative structure is possible to obtain an uncertainty region D(P) determined on the Pareto plane. The region D(P) is converted into parametric uncertainty that can be used in robust control methods.