Parameter reduction of nonlinear least-squares estimates via the singular value decomposition

This paper proposes a technique for reducing the number of uncertain parameters in order to simplify robust and adaptive controller design. The system is assumed to have a known structure with parametric uncertainties that represent plant dynamics variation. An original set of parameters is identified by nonlinear least-squares (NLS) optimization using noisy frequency response functions. Using the property of asymptotic normality for NLS estimates, the original parameter set is re-parameterized by an affine function of the smaller number of uncorrelated parameters. The correlation among uncertain parameters over NLS estimates from different plants is detected by the singular value decomposition. A numerical example illustrates the usefulness of the proposed techniques.