Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We validate the proposed method in simulation with an inverted pendulum in multiple experimental configurations.

中文翻译：

---

致动不确定非线性系统的鲁棒数据驱动控制综合

现代非线性控制理论试图赋予系统稳定性和安全性等特性，并已成功地在各个领域中得到应用。尽管取得了成功，但模型不确定性仍然是确保基于模型的控制器转移到实际系统中的重大挑战。本文开发了一种数据驱动的方法，用于在存在模型不确定性的情况下使用控制证书功能（CCF）进行鲁棒的控制综合，从而得出了基于凸优化的控制器，以实现稳定性和安全性等属性。我们的框架的一个重要好处是细微的数据相关保证，从原则上讲，它可以提供无需完全确定输入与状态关系的样本有效数据收集方法。这项工作是解决非线性控制理论与非参数学习在理论上和应用上相交的重要问题的起点。我们在多个实验配置中的倒立摆仿真中验证了所提出的方法。