Data-driven Stabilization of SISO Feedback Linearizable Systems

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.