Parameter reduction of nonlinear least-squares estimates via nonconvex optimization

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 reparameterized by an affine function of the smaller number of uncorrelated parameters. The correlation among uncertain parameters is detected by optimization with a bilinear matrix inequality. A numerical example illustrates the usefulness of the proposed technique.