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

Many data-driven control methodologies depend on an initial stabilizing control policy, and subsequently use operational data to refine the initial policy in order to optimize closed-loop performance. For general dynamical systems, computing such an initial policy is non-trivial, and systematic methods for this task are not available in the current literature. In this paper, we propose a systematic framework for constructing stabilizing and/or constraint-enforcing control policies for a class of nonlinear systems based on archival data. Specifically, we study partially unmodeled systems whose nonlinearities satisfy local Lipschitz conditions. We employ kernel density estimation (KDE) to learn a local Lipschitz constant from archival data, and compute control policies by solving semidefinite programs that leverage matrix multipliers informed by the Lipschitz learner. We demonstrate the potential of our proposed methodology on a nonlinear system with unmodeled dynamics.