Estimation of states and parameters for linear systems with nonlinearly parameterized perturbations

We consider systems that can be described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. Under a set of technical assumptions about the perturbation and its relationship to the outputs, we present a modular design technique for estimating the system states and the unknown parameters. The design consists of a high-gain observer that estimates the states of the system together with the full perturbation, and a parameter estimator constructed by the designer to invert a nonlinear equation. We illustrate the technique on a simulated dc motor with friction.