  In this paper we propose a methodology for stabilizing single-input
single-output feedback linearizable systems when no system model is known and
no prior data is available to identify a model. Conceptually, we have been
greatly inspired by the work of Fliess and Join on intelligent PID controllers
and the results in this paper provide sufficient conditions under which a
modified version of their approach is guaranteed to result in asymptotically
stable behavior. One of the key advantages of the proposed results is that,
contrary to other approaches to controlling systems without a model (or with a
partial model), such as reinforcement learning, there is no need for extensive
training nor large amounts of data. Technically, our results draw heavily from
the work of Nesic and co-workers on observer and controller design based on
approximate models. Along the way we also make connections with other well
established results such as high-gain observers and adaptive control. Although
we focus on the simple setting of single-input single-output feedback
linearizable systems we believe the presented results are already theoretically
insightful and practically useful, the last point being substantiated by
experimental evidence.
