Dissipativity-Preserving Reduced-Order Modeling from Data

Reduced-order modeling from data with dissipativity preservation is discussed in this talk. Employing the data informativity framework, the dissipativity of all systems consistent with noisy data can be characterized by a data-based linear matrix inequality (LMI). Furthermore, semi-definite programming duality helps us to prove the existence of minimal and maximal solutions to the LMI. As in the classical bounded-real and positive-real balanced truncation, these extremal solutions play a role in the computation of well-approximating reduced-order models carrying the dissipativity property. As an additional advantage of using this balancing-type method, a priori error bounds of the reduced-order models are available.