Forward Invariance

Forward invariance, in the context of dynamical systems, focuses on guaranteeing that a system's trajectory remains within a predefined safe set of states over time. Current research emphasizes developing methods to ensure forward invariance, particularly in complex systems controlled by neural networks or reinforcement learning agents, often employing techniques like control barrier functions and interval analysis to provide provable safety guarantees. This research is crucial for deploying autonomous systems in safety-critical applications, such as robotics and autonomous driving, by providing robust and verifiable safety assurances. The development of efficient algorithms and frameworks for certifying forward invariance is driving progress in reliable and trustworthy AI.