Data-driven Stabilization of Unknown Feedback-Linearizable and Partially Feedback-Linearizable Systems

This thesis reports on my research in data-driven control, addressing the problem of data-driven stabilization, i.e., stabilization of unknown nonlinear systems without making explicit use of a model. Broadly speaking, it's aim is to answer the question: can we design simple plug-and-play controllers to streamline a control engineer's work? While the trivialization of a controls engineering is probably out of anyone's reach, and most certainly out of mine, I focus on a special class of systems. These are general enough to be practically useful, yet well-behaved to the point of making the problem at hand tractable. My hope is to simplify the design of low-level controllers thus reducing the need for, among other things, hardware-specific controller design, allowing the engineer to focus primarily on the high-level control task. To that end, this work focuses primarily on single-input single-output (SISO) feedback linearizable and partially-feedback linearizable systems with stable or input-to-state stable (ISS) zero-dynamics. We start by considering the stabilization of the former, something accomplished by requiring only a minimal amount of real-time output data and without the need for persistency of excitation. This is achieved through a novel understanding of how to guarantee the asymptotic stability of unknown continuous-time systems through the use of families of approximate discrete-time models and Lyapunov-based techniques. It follows by expanding onto the multiple-input multiple-output extension and introducing dirty derivatives as a derivative estimation technique with the aim of ameliorating the method's sensitivity to measurement noise. Finally, it concludes by presenting a strikingly simple continuous-time controller capable of stabilizing SISO feedback linearizable and partially-feedback linearizable systems with ISS zero-dynamics. This controller is constructed resorting to well-known techniques, a linear observer and a linear dynamic controller. Based on the simplicity of the methods here developed, the stability guarantees provided and their need of minimal knowledge of the underlying system, I believe they will find future use in practical applications