Estimation and Control for Systems with Nonlinearly Parameterized Perturbations

A class of systems influenced by nonlinearly parameterized perturbations is considered. An estimation scheme is developed whereby exponentially stable estimates of the unknown parameters can be obtained with an arbitrarily large region of attraction, provided the states are available for measurement. The method applies to a class of perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known. Compensation for the perturbations in the system equations is considered for a class of systems which have uniformly globally bounded solutions and for which the origin is globally asymptotically stable when no perturbations are present. Examples with simulations are given in order to illustrate the results.