Interconnection-based model order reduction for quadratic-bilinear systems

Abstract

This thesis addresses the problem of model order reduction for quadratic-bilinear systems through an interconnection-based methodology. Initially, we compute the nonlinear moments for this type of systems by utilizing a formal power series representation. Two families of reduced-order model are proposed to achieve moment matching at specific interpolation points, while maintaining some key properties of the original system. Based on the model-based strategy, we then apply a data-driven algorithm to achieve reduced-order models by moment matching, using input and output data. This dual approach, both model-based and data-driven, is applied to the task of model order reduction for incompressible flows derived directly from the Navier-Stokes equations. Subsequently, we extend this approach to quadratic-bilinear time-delay systems by matching an approximated moment, achieved by truncating the power series. We present findings for both time-delay and non-time-delay systems represented in polynomial form. Finally, we introduce a two-sided interconnection for the model order reduction of quadratic-bilinear systems. This approach effectively doubles the number of matched moments in reduced-order models of the same size by considering both ``direct'' and ``swapped'' moments. We propose two families of reduced-order models: the first is designed based on the idea for general nonlinear systems, and the second leverages power series approximations.