Expanding the Safety Envelope: Adaptive Control with Backup Barrier Functions
A new generalization of backup control barrier functions allows for larger safe operating regions and online adaptation, improving the safety and performance of control systems with input limitations.



![The system distills a raw stream of 6.27 million Ethereum transactions-initially filtered to identify potential Ethscriptions-down to a focused analytical set of 4.75 million ([latex]U\_2[/latex]), representing 75.8% of the initial candidates, through MIME classification, JSON validation, and grammatical parsing-a process that prioritizes data integrity and contextual relevance as the foundation for subsequent measurement.](https://arxiv.org/html/2603.19086v1/img/fig_methodology_v3_1.png)