Structure-Preserving Linear Quadratic Gaussian Balanced Truncation for Port-Hamiltonian Descriptor Systems

by   Tobias Breiten, et al.

We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that arise in the context of linear quadratic Gaussian balanced truncation for differential algebraic systems. We derive an a priori error bound with respect to a right coprime factorization of the underlying transfer function thereby allowing for an estimate with respect to the gap metric. We further theoretically and numerically analyze the influence of the Hamiltonian and a change thereof, respectively. With regard to this change of the Hamiltonian, we provide a novel procedure that is based on a recently introduced Kalman-Yakubovich-Popov inequality for descriptor systems. Numerical examples demonstrate how the quality of reduced-order models can significantly be improved by first computing an extremal solution to this inequality.


page 1

page 2

page 3

page 4


Passivity preserving model reduction via spectral factorization

We present a novel model-order reduction (MOR) method for linear time-in...

Control of port-Hamiltonian differential-algebraic systems and applications

The modeling framework of port-Hamiltonian descriptor systems and their ...

A Rosenbrock framework for tangential interpolation of port-Hamiltonian descriptor systems

We present a new structure-preserving model order reduction (MOR) framew...

Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

We present a numerical approach for approximating unknown Hamiltonian sy...

Reciprocal and Positive Real Balanced Truncations for Model Order Reduction of Descriptor Systems

Model order reduction algorithms for large-scale descriptor systems are ...

Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems

When computing the eigenstructure of matrix pencils associated with the ...

Canonical and Noncanonical Hamiltonian Operator Inference

A method for the nonintrusive and structure-preserving model reduction o...

Please sign up or login with your details

Forgot password? Click here to reset