Symplectic model order reduction of port-Hamiltonian systems

Abstract This work proposes a novel structure-preserving model reduction () method for linear, time-invariant port-Hamiltonian () systems. Our goal is to construct a reduced-order system, which can still be interpreted in the physical domain of the full order model. By this we mean, that if an electrical circuit is the initial high-dimensional system, we want the reduced-order model to be still interpretable as an electronic circuit. In the case of the well-known mass spring damper () system, there are methods available, which already guarantee the preservation of this particular structure. Moreover, we show that our new structure-preserving method, which is based on symplectic methods, will recover the known second-order Arnoldi method in the case of systems. However, for the example of an electrical circuit model (and more models of similar block structure), our method yields a novel model reduction method. We present numerical results on the aforementioned electronic circuit model, highlighting the advantages of the proposed method.