Safe control with guarantees generally requires the system model to be known. It is far more challenging to handle systems with uncertain parameters. In this paper, we propose a generic algorithm that can synthesize and verify safe controllers for systems with constant, unknown parameters. In particular, we use robust-adaptive control barrier functions (raCBFs) to achieve safety. We develop new theories and techniques using sum-of-squares that enable us to pose synthesis and verification as a series of convex optimization problems. In our experiments, we show that our algorithms are general and scalable, applying them to three different polynomial systems of up to moderate size (7D). Our raCBFs are currently the most effective way to guarantee safety for uncertain systems, achieving 100% safety and up to 55% performance improvement over a robust baseline.

翻译：具有保障的安全控制通常需要系统模型已知，而处理参数不确定的系统则更具挑战性。本文提出一种通用算法，能够对具有恒定未知参数的系统实现安全控制器的综合与验证。具体而言，我们采用鲁棒自适应控制障碍函数（raCBF）来保障安全性。通过开发基于平方和的新理论与技术，我们将综合与验证问题转化为一系列凸优化问题。实验表明，我们的算法具有通用性和可扩展性，可应用于三个不同阶次（最高7维）的多项式系统。当前，raCBF是保障不确定系统安全性的最有效方法，在实现100%安全性的同时，相比鲁棒基线方法性能提升高达55%。