Nonlinear Bounded-Error Parameter Estimation Using Interval Computation

This paper deals with the estimation of the parameters of a model from experimental data. The aim of the method presented is to characterize the set S of all values of the parameter vector that are acceptable in the sense that all errors between the experimental data and the corresponding model outputs lie between known lower and upper bounds. This corresponds to what is known as bounded-error estimation or membership-set estimation. Most of the methods available to give guaranteed estimates of S rely on the hypothesis that the model output is linear in its parameters, contrary to the method advocated here which can deal with nonlinear models. This is made possible by the use of the tools of interval analysis, combined with a branch-and-bound algorithm. The purpose of the present paper is to show that the approach can be cast into the more general framework of granular computing.