Towards data-driven control of general nonlinear systems with stability and performance guarantees

While in recent years, learning-based and data-driven methods have shown rapid progress in effective utilization of data for control tasks, the focus has mainly be on the analysis and control of linear time-invariant (LTI) systems or rather restricted forms of nonlinear systems. In this talk, I will present a direct data-driven control paradigm for a rather wide class of nonlinear systems. To establish this, we first take an intermediate step via linear parameter-varying (LPV) surrogates of nonlinear systems. The first part of the talk will go over the data-driven tools that we have developed for LPV systems, such as the LPV Fundamental Lemma, dissipativity analysis, predictive control and state-feedback control. In the second part of the we propose a data-driven control scheme for a wide class of  nonlinear systems by combining the LPV data-driven tools with velocity-based control of nonlinear systems (that is linked to paradigms such as universal shifted stability). A key ingredient of the method is a data-driven representation of the velocity-form (the time-difference dynamics) of the nonlinear system, which admits a direct LPV representation, that can be used for direct data-driven control. By using a realization approach, the synthesized data-driven LPV controller for the velocity-form is realized for the original nonlinear system as a nonlinear controller, which guarantees universal shifted stability and dissipativity of the closed-loop. In addition to the theoretical results, I will also present successful applications of the proposed framework in simulation studies and real-world experiments.