A convex approximation of the feasible solution set for nonlinear bounded-error identification problems

A new nonlinear bounded-error identification method is presented in this paper. We consider models that depend non linearly on a given set of parameters. An additive bounded error term is included to take into account non modelled dynamics and disturbances in the measurements. The objective of the proposed methodology is to obtain the set of parameters that are consistent with a sequence of input- output measurements and the additive bounded error term. An iterative algorithm that provides a sequence of polyhedral outer bounds of this set is presented. At each iteration, a new improved outer bound is obtained adding some linear constraints to those defining the previous polyhedral outer bound. In this way, the volume of the outer approximation is shown to decrease at each iteration. The results of the paper rely on the representation of the functional form of the system by means of the difference of convex functions. An example is provided to illustrate the algorithm.