Some problems arising in controller design from big data via input-output methods

Jan Maximilian Montenbruck, Frank Allgöwer

Abstract: We study problems arising when attempting to apply classical input-output techniques for controller design to systems from which one only drew finitely many (input-output) samples. Such problems arise in controller design for big data applications. In particular, we derive overestimates on the operator norm, the shortage of passivity, and the cone containing the input-output tuples, all solely from our finite input-output data. This allows for application of the small-gain theorem, the feedback theorem for passive systems, and the feedback theorem for conic relations.