Data-driven inference of passivity properties via Gaussian process optimization

Passivity is an important concept in control design as it pertains to stability properties of the closed loop. We propose a framework to determine to which extent a dynamic system is or is not passive from data. In particular, we develop a probabilistic approach based on Gaussian processes to underestimate the input feedforward passivity index from experiments with measurement noise. We also show how prior knowledge on the input-output behavior can be incorporated in this framework. Besides the offline approach, we present an iterative scheme that in expectation tightens the lower bound on the feedforward passivity index with every additional data sample and gives an upper bound on the conservatism of the resulting passivity measure.