Non-linear dynamics in adaptive control: Chaotic and periodic stabilization

Al~tract--In this paper the non-linear features of adaptive control algorithms are highlighted. Using a simple "linear" discrete time example, based on classical design, it is demonstrated that in the presence of undermodelling errors, non-linear phenomena in the feedback gain such as limit cycles and even chaos arise. Despite these complicated dynamics, robust stabilization of the plant can still occur. For the class of undermodelling errors considered, the set of plants stabilizable by this adaptive controller is completely characterized.