From data to reduced-order models of complex dynamical systems

Abstract

Modeling of dynamical systems is at the core of the simulation and controller design of modern technological products and processes. Due to the ever-increasing demand for accuracy and ever-larger scale of engineering systems, the model complexity of dynamical systems naturally increases as well, described by their dimension or order. This can lead to unmanageably enormous demands on computational resources and time for simulation or analysis. Hence, approximating a complex system with a reduced-order model with low complexity is desirable. This is where model reduction methods come into play. This topic has been studied for decades and classically performed by reducing the order of a given high-dimensional state-space model. However, there are situations where the high-dimensional model of a complex system is difficult or time-consuming to access, but the data observed from it are accessible. Hence, this thesis mainly addresses reduced-order modeling from data without identifying the high-order model. Further, the preservation of key system-properties satisfied by the original system is an essential aspect of the reduced-order modeling. This thesis considers three properties to be preserved using data observed from unknown systems: transfer function moments, stability, and dissipativity; additionally, the preservation of structure of network systems is studied. For dealing with data, we approach the problem from the angle of data informativity, which enables us to guarantee that the unknown system has the desired property.