Structure-preserving interpolation for model reduction of parametric bilinear systems

Structure Preserving Model Reduction of Parametric Hamiltonian Systems

While reduced-order models (ROMs) are popular for approximately solving large 4 systems of differential equations, the stability of reduced models over long-time integration remains 5 an open question. We present a greedy approach for ROM generation of parametric Hamiltonian 6 systems which captures the symplectic structure of Hamiltonian systems to ensure stability of the 7 reduced model. Thro...

Interpolation Methods for the Model Reduction of Bilinear Systems

Implicit Volterra series interpolation for model reduction of bilinear systems

We propose a new interpolatory framework for model reduction of largescale bilinear systems. The input-output representation of a bilinear system in frequency domain involves a series of multivariate transfer functions, each representing a subsystem of the bilinear system. If a weighted sum of these multivariate transfer functions associated with a reduced bilinear system interpolates a weighte...

Interpolation-Based H2-Model Reduction of Bilinear Control Systems

In this paper, we will discuss the problem of optimal model order reduction of bilinear control systems with respect to the generalization of the well-known H2norm for linear systems. We revisit existing first order necessary conditions for H2-optimality based on the solutions of generalized Lyapunov equations arising in bilinear system theory and present an iterative algorithm which, upon conv...

Structure-preserving model reduction for mechanical systems

This paper focuses on methods of constructing of reduced-order models of mechanical systems which preserve the Lagrangian structure of the original system. These methods may be used in combination with standard spatial decomposition methods, such as the Karhunen–Loève expansion, balancing, and wavelet decompositions. The model reduction procedure is implemented for three-dimensional finite-elem...