Learning-enabled control systems have demonstrated impressive empirical performance on challenging control problems in robotics, but this performance comes at the cost of reduced transparency and lack of guarantees on the safety or stability of the learned controllers. In recent years, new techniques have emerged to provide these guarantees by learning certificates alongside control policies -- these certificates provide concise, data-driven proofs that guarantee the safety and stability of the learned control system. These methods not only allow the user to verify the safety of a learned controller but also provide supervision during training, allowing safety and stability requirements to influence the training process itself. In this paper, we provide a comprehensive survey of this rapidly developing field of certificate learning. We hope that this paper will serve as an accessible introduction to the theory and practice of certificate learning, both to those who wish to apply these tools to practical robotics problems and to those who wish to dive more deeply into the theory of learning for control.

翻译：学习辅助控制系统在应对机器人控制问题方面表现出了令人印象深刻的经验性表现,但这种表现的代价是透明度降低,对学习的控制者的安全或稳定缺乏保障。近年来,出现了通过学习证书以及控制政策提供这些保障的新技术 -- -- 这些证书提供了保证学习控制系统的安全和稳定的简明、数据驱动的证明。这些方法不仅允许用户核查学习过的控制者的安全,而且允许在培训期间进行监督,允许安全和稳定要求影响培训过程本身。我们在本文件中对迅速发展的证书学习领域进行了全面调查。我们希望,这份文件将成为证书学习理论和实践的一个方便的介绍,既向那些希望将这些工具应用于实际机器人问题的人,也向那些希望深入学习控制理论的人,介绍证书学习理论和实践。