Generic properties of universal adaptive stabilization schemes

Two problems in non-identifier-based adaptive control are considered. They are the related problems of stability of solutions under small perturbations of the initial data, and possible stabilization by the limiting gain. For the class of adaptation schemes that are of the switching sequence type, it is shown using a topological approach, that the set of initial conditions for which solutions are stable under small perturbations and the limiting gain is stabilizing, has dense interior. The results are illustrated with examples of planar control systems