Active Informativity: Online Input Design for Data-Driven Control

We develop a unified framework for online input design in data-driven control from noisy data. We introduce a performance measure and analyze how such quality measure changes as new data are added. Based on such analysis we propose an online method for selecting inputs that ensures that data quality does not decrease over time. We demonstrate the validity of our approach by formulating six common noisy data-driven control problems in our framework, and by solving numerical examples for three of them.