Parameter Optimization for Learning-based Control of Control-Affine Systems

Supervised machine learning is often applied to identify system dynamics where first principle methods fail. When combining learning with control methods, probabilistic regression is typically applied to increase robustness against learning errors. Although this combination of probabilistic regression and control theory allows to formulate performance guarantees for many control techniques, the bounds are usually conservative, and cannot be employed for efficient control parameter tuning. Therefore, we reformulate the parameter tuning problem using robust optimization with performance constraints based on Lyapunov theory. By relaxing the problem through scenario optimization, we derive a with high probability optimal method for control parameter tuning. We demonstrate its flexibility and efficiency on parameter tuning problems for a feedback linearizing and a computed torque controller.