Constrained optimal reduced-order models from input/output data - Scarciotti,G; Astolfi,A; Jiang,Z-P (IEEE, 2016)
Model reduction by moment matching does notpreserve, in a systematic way, the transient response of thesystem to be reduced, thus limiting the use of this modelreduction technique in control problems. With the final goalof designing reduced-order models which can effectively beused (not just for analysis but also) for control purposes, wedetermine, using a data-driven approach, an estimate of themoments and of the transient response of an unknown system.We compute the unique, up to a change of coordinates, reducedordermodel which possesses the estimated transient and,simultaneously, achieves moment matching at the prescribedinterpolation points. The error between the output of the systemand the output of the reduced-order model is minimized andwe show that the resulting system is a constrained optimal (ina sense to be specified) reduced-order model. The results of thepaper are illustrated by means of a simple numerical example.