Many existing tools in nonlinear control theory for establishing stability or
safety of a dynamical system can be distilled to the construction of a
certificate function that guarantees a desired property. However, algorithms
for synthesizing certificate functions typically require a closed-form
analytical expression of the underlying dynamics, which rules out their use on
many modern robotic platforms. To circumvent this issue, we develop algorithms
for learning certificate functions only from trajectory data. We establish
bounds on the generalization error - the probability that a certificate will
not certify a new, unseen trajectory - when learning from trajectories, and we
convert such generalization error bounds into global stability guarantees. We
demonstrate empirically that certificates for complex dynamics can be
efficiently learned, and that the learned certificates can be used for
downstream tasks such as adaptive control.

我们开发了一种算法，从轨迹数据中学习证明函数。我们从轨迹数据中建立了证明函数，并将其转换为全局稳定性保证，可以应用于其他任务中。

从数据中学习稳定证明

Learning Stability Certificates from Data

Modern nonlinear control theory seeks to endow systems with properties of
stability and safety, and have been deployed successfully in multiple domains.
Despite this success, model uncertainty remains a significant challenge in
synthesizing safe controllers, leading to degradation in the properties
provided by the controllers. This paper develops a machine learning framework
utilizing Control Barrier Functions (CBFs) to reduce model uncertainty as it
impact the safe behavior of a system. This approach iteratively collects data
and updates a controller, ultimately achieving safe behavior. We validate this
method in simulation and experimentally on a Segway platform.

利用控制屏障函数的机器学习框架可以降低非线性控制系统中的模型不确定性，从而实现系统的安全行为。通过在 Segway 平台上进行模拟和实验验证，这种方法可以持续收集数据并更新控制器，最终实现安全行为。