Barrier Function

Barrier functions are mathematical tools used to guarantee the safety of dynamical systems, ensuring that a system's trajectory remains within a predefined safe set. Current research focuses on developing robust barrier function methods for systems with noise, disturbances, and uncertain dynamics, employing techniques like Gaussian process regression, resilient estimators, and neural networks to learn and adapt barrier functions from data. This work is crucial for enabling safe and reliable operation of autonomous systems in various applications, including robotics, control systems, and self-driving vehicles, by providing provable safety guarantees even under uncertainty. The development of efficient algorithms for synthesizing and verifying barrier functions, particularly for high-dimensional systems, remains a key area of ongoing investigation.