Parametric Model Order Reduction of Port-Hamiltonian Systems by Matrix Interpolation

Abstract

Abstract:In this paper, parametric model order reduction of linear time-invariant systems by matrix interpolation is adapted to large-scale systems in port-Hamiltonian form. A new weighted matrix interpolation of locally reduced models is introduced in order to preserve the portHamiltonian structure, which guarantees the passivity and stability of the interpolated system.

STABLE – a stability algorithm for parametric model reduction by matrix interpolation

“…The transformation matrices for adjusting the right ROBs are calculated using the MAC or DS approach minimizing the objective function (Equation (7) or (8) (10)). The local systems are transformed according to Equation (11) and result in the systemsG WS ¼ fG interpolating the systems of the setG WS according to Equations (12) and (13) using bilinear weighting functions. For testing the system, we compute the error in H 1 -norm at the points of a test grid P test ¼ f0; 1=80; .…”

“…Stability-preserving matrix interpolation for dissipative systems is suggested in [11], for PortHamiltonian systems in [12] and for passive systems in [13,14]. Concerning the general class of linear time-invariant (LTI) systems, a technique is suggested in [15,16] for passivity-preserving parameterized MOR which exploits the solution of high-order linear matrix inequalities (LMIs).…”

“…. ;G 36 g. The parametric reduced systemGðpÞ is obtained by interpolating the systems of the setG according to Equations (12) and (13) using bilinear weighting functions. The error e P test H 1 : P test !…”

A Black-Box method for parametric model order reduction based on matrix interpolation with application to simulation and control

“…In [11], stable interpolation on matrix manifolds is proposed for systems of ODE in second-order form. Stability-preserving matrix interpolation for dissipative systems is suggested in [55], for Port-Hamiltonian systems in [78] and for passive systems in [61,58]. All these methods are efficient because they can make use of Corollary 2.2 as the structure of the considered high-order systems meets the associated requirements.…”

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

“…In this context, structure-preserving model order reduction for port-Hamiltonian (pH) systems is a frequently used approach to ensure a stable and passive reduced-order model, see e.g. [8,9,10,14,16,17,28] for the case without algebraic constraints and [4,13,18] for the DAE case. The Port-Hamiltonian structure is particularly useful for model reduction since it ensures passivity and under certain assumptions for the Hamiltonian also stability, see for instance [34, sec.…”