Robust Data-Driven Control for Nonlinear Systems Using their Digital Twins and Quadratic Funnels

This paper examines a robust data-driven approach for the safe deployment of systems with nonlinear dynamics using their imperfect digital twins. Our contribution involves proposing a method that fuses the digital twin's nominal trajectory with online, data-driven uncertainty quantification to synthesize robust tracking controllers. Specifically, we derive data-driven bounds to capture the deviations of the actual system from its prescribed nominal trajectory informed via its digital twin. Subsequently, the dataset is used in the synthesis of quadratic funnels -- robust positive invariant tubes around the nominal trajectory -- via linear matrix inequalities built on the time-series data. The resulting controller guarantees constraint satisfaction while adapting to the true system behavior through a segmented learning strategy, where each segment's controller is synthesized using uncertainty information from the previous segment. This work establishes a systematic framework for obtaining safety certificates in learning-based control of nonlinear systems with imperfect models.