Preprint 02-2019

Model reduction techniques for linear constant coefficient port-Hamiltonian differential-algebraic systems

Author(s) : Sarah-Alexa Hauschild , Nicole Marheineke , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 02-2019

MSC 2000

34H05 Control problems

41A20 Approximation by rational functions

Abstract :
Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the state space dimension of such systems may be very large, in particular when the model is a space-discretized partial differential-algebraic system, in optimization and control there is a need for model reduction methods that preserve the port-Hamiltonian structure while keeping the (explicit and implicit) algebraic constraints unchanged. To combine model reduction for differential-algebraic equations with port-Hamiltonian structure preservation, we adapt two classes of techniques (reduction of the Dirac structure and moment matching) to handle port-Hamiltonian differential-algebraic equations. The performance of the methods is investigated for benchmark examples originating from semi-discretized flow problems and mechanical multibody systems.

Keywords : structure-preserving model reduction, index reduction, port-Hamiltonian differential-algebraic system, moment matching, effort constraint method, flow constraint method