Wasserstein Geometry-Aware Adaptive Control via Meta-Learning

Abstract

Adaptive control of nonlinear systems under unknown disturbances requires learning algorithms aligned with the downstream control objective. While control-oriented meta-learning addresses the mismatch between regression-based identification and tracking performance, existing methods rely on Euclidean or static algebraic geometries that fail to capture the distributional structure of system uncertainties. We propose a framework that lifts adaptation into Wasserstein space, measuring parameter estimation errors as the optimal transport cost between estimated and true system behaviors. By constructing a Wasserstein Bregman divergence over representative task distributions, we use meta-learning to jointly optimize nonlinear feature representations, control gains, and transport geometry. This adaptation law learns an adaptation geometry that captures structural properties of the underlying physical system, implementing a physically grounded, data-driven attention mechanism. Closed-loop tracking simulations demonstrate that our controller achieves optimal performance on both fully-actuated and underactuated nonlinear planar rotorcraft, maintaining robustness under significant distributional shifts between training and testing conditions.