Structure-preserving model reduction of complex physical systems

Abstract

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Balanced Realizations, Model Order Reduction, and the Hankel Operator

“…Recently, a lot of interest is taken in structure preserving order techniques for both linear and nonlinear systems, where the additional structure to be preserved is a physical structure, such as port-Hamiltonian structure, [56], and other physical structures, as mentioned in our linear systems section. For example, for circuit simulators with continuously growing orders of the models, a need for interpreting a reduced order model as a circuit is important, such as, [50].…”

Approximation of stability radii for large-scale dissipative Hamiltonian systems

“…In this subsection we derive an interpolating, DH structure preserving version of the robust subspace projection framework. Structure preserving subspace projection methods in the context of model order reduction of large-scale PH and DH systems have been proposed in [10,11,17,18,21,22]. Our approach is inspired by [10] and uses a general interpolation result from [6].…”

Discussion on: “Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces”

“…The port-Hamiltonian approach to modeling and control of complex physical systems has arisen as a systematic and unifying framework during the last twenty years, see [11], [7], [12], [2] and the references therein. The portHamiltonian modeling captures the physical properties of the considered system including the energy dissipation, stability and passivity properties as well as the presence of conservation laws.…”