In control design, cost functions are used to encode performance objectives, such as energy efficiency, tracking accuracy, or robustness. However, with the increasing complexity of modern systems, it remains challenging for controllers to optimize complicated, non-convex cost functions while still guaranteeing safety and stability. Classical control methods—such as Model Predictive Control—provide rigorous analyses for closed-loop stability and constraint satisfaction, yet they often limit the joint design of rich cost functions and stability properties. Although learning-based control approaches optimize performance through their rich flexibility, their blackbox nature makes satisfying hard constraints difficult. Recent work on the performance boosting problem 1, 2 has introduced control parameterizations that maintains closed-loop stability under even learning-based methods. Meanwhile, the Predictive Safety Filter leverages Model Predictive Control theory to enable safe learning under constraints. This thesis advances the performance boosting control scheme by proposes a novel framework that embeds a modified Predictive Safety Filters to deliver guarantees of stability and constraint satisfaction while retaining suboptimal performance. We provide a formal investigation of stability guarantees and explore various differentiation methods for the training process, including direct differentiation and Reinforcement Learning approximation. The effectiveness of the proposed approach is demonstrated on a single-pendulum stabilization task, where a moving obstacle traverses horizontally across the swing-up position, showing that safety and stability can be maintained while ensuring obstacle-avoidance performance. Overall, the proposed method decouples control design objectives, offering a promising path to leverage learning-based methods and enhance existing controllers.
Haoming Shen (Wed,) studied this question.