UC San Diego

This dissertation introduces a form of extremum seeking, traditionally employed for optimizing unknown objective functions, now adapted to accommodate an unknown yet measurable constraint. We consider the constraint to be a safety metric, which is maintained, practically, throughout the optimization process. We demonstrate that our approach can ensure safety violations be made arbitrarily small, parallel to how classical extremum seeking controllers achieve stability near optimal points. The power of this algorithm is particularly underscored in its application to particle accelerator systems, shown in several examples, where safety is critical to prevent substantial financial losses and operational downtime. This work broadens the scope of extremum seeking methods and establishing an approach for integrating safety considerations into optimization processes, useful in situations where balancing optimal performance with stringent safety requirements is essential.