Data-Driven Control Policies for Partially Known Systems via Kernelized Lipschitz Learning

Generating initial stabilizing control policies that satisfy operational constraints in the absence of full model information remains an open but critical challenge. In this paper, we propose a systematic framework for constructing constraint enforcing initializing control policies for a class of nonlinear systems based on archival data. Specifically, we study systems for which we have linear components that are modeled and nonlinear components that are unmodeled, but satisfy a local Lipschitz condition. We employ kernel density estimation (KDE) to learn a local Lipschitz constant from data (with high probability), and compute a constraint enforcing control policy via matrix multipliers that utilizes the learned Lipschitz constant. We demonstrate the potential of our proposed methodology on a nonlinear system with an unmodeled local Lipschitz nonlinearity.