Synthesizing safety controllers for general nonlinear systems is a highly challenging task, particularly when the system models are unknown, and input constraints are present. While some recent efforts have explored data-driven safety controller design for nonlinear systems, these approaches are primarily limited to specific classes of nonlinear dynamics (e.g., polynomials) and are not applicable to general nonlinear systems. This paper develops a direct data-driven approach for discrete-time general nonlinear systems, facilitating the simultaneous learning of control barrier certificates (CBCs) and dynamic controllers to ensure safety properties under input constraints. Specifically, by leveraging the adding-one-integrator approach, we incorporate the controller's dynamics into the system dynamics to synthesize a virtual static-feedback controller for the augmented system, resulting in a dynamic safety controller for the actual dynamics. We collect input-state data from the augmented system during a finite-time experiment, referred to as a single trajectory. Using this data, we learn augmented CBCs and the corresponding virtual safety controllers, ensuring the safety of the actual system and adherence to input constraints over a finite time horizon. We demonstrate that our proposed conditions boil down to some data-dependent linear matrix inequalities (LMIs), which are easy to satisfy. We showcase the effectiveness of our data-driven approach through two case studies: one exhibiting significant nonlinearity and the other featuring high dimensionality.

This work is concerned with a data-driven scheme to construct reduced-order models (ROMs) of dynamical systems with unknown mathematical models. Our methodology leverages data and establishes similarity relations between output trajectories of unknown systems and their data-driven ROMs via the notion of simulation functions (SFs), capable of formally quantifying their closeness. To achieve this, under a rank condition readily fulfillable using data, we collect only two input-output trajectories from unknown systems to construct both ROMs and SFs, while offering correctness guarantees. We demonstrate that the proposed ROMs derived from data can be leveraged for controller synthesis endeavors while effectively ensuring high-level logic properties over unknown dynamical models. We showcase our data-driven findings across a range of benchmark scenarios involving various unknown physical systems, demonstrating the enforcement of diverse complex properties.