ETD

• Distributionally robust control
• Nonlinear control
• Sinkhorn

This thesis investigates the design of learning-based controllers for nonlinear dynamical systems whose performance is affected by uncertain disturbances. In many control applications, stability alone is not sufficient, and the controller must also improve transient behavior or achieve additional objectives such as tracking, constraint satisfaction, or robustness to changing operating conditions. Existing performance-boosting approaches often rely on the assumption that the disturbance distribution is known, which is rarely realistic when only finite data are available.
The goal of this work is to study a distributionally robust formulation of the performance-boosting control problem. Instead of optimizing the controller only with respect to an empirical distribution of observed disturbances, the proposed approach considers a family of plausible distributions around the available data and optimizes against the worst-case member of this family. This provides a principled way to reduce sensitivity to sampling error and improve generalization to unseen scenarios.
The thesis focuses on formulating the distributionally robust training scheme, analyzing its main properties, and implementing numerical experiments to assess its behavior on nonlinear control examples. The emphasis is on developing a flexible framework that combines performance improvement with robustness to distributional uncertainty.