Multiobjective parameter estimation for non-linear systems: affine information and least-squares formulation

Abstract

This paper defines a class of system information—affine information—that includes both the dynamic residuals and some types of auxiliary information that can be used in system parameter estimation as special cases. The types of information that can be cast under the affine information format give rise to quadratic functions that measure the extent to which a model fits such information, and that can be aggregated in a single weighted quadratic cost functional. This allows the definition of a multiobjective methodology for parameter estimation in non-linear system identification, which allows taking into account any type of affine information. The results are presented in terms of a set of efficient solutions of the multiobjective estimation problem—such a solution set is more meaningful than a single model. Since any affine information leads to a convex (quadratic) functional, the whole set of efficient solutions is exactly accessible via the minimization of the quadratic functional with different weightings, via a least-squares minimization (a non-iterative, computationally inexpensive procedure). The decision stage, in which a single model is chosen from the Pareto-set, becomes well-defined with a single global solution. Residual variance, fixed point location, static function and static gain are shown to fit in the class of affine information. A buck DC-DC converter is used as example.