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Learning-enabled control systems have demonstrated impressive empiricalperformance on challenging control problems in robotics, but this performancecomes at the cost of reduced transparency and lack of guarantees on the safetyor stability of the learned controllers. In recent years, new techniques haveemerged to provide these guarantees by learning certificates alongside controlpolicies -- these certificates provide concise, data-driven proofs thatguarantee the safety and stability of the learned control system. These methodsnot only allow the user to verify the safety of a learned controller but alsoprovide supervision during training, allowing safety and stability requirementsto influence the training process itself. In this paper, we provide acomprehensive survey of this rapidly developing field of certificate learning.We hope that this paper will serve as an accessible introduction to the theoryand practice of certificate learning, both to those who wish to apply thesetools to practical robotics problems and to those who wish to dive more deeplyinto the theory of learning for control.

Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods