Structure Preserving Truncation of Nonlinear Port Hamiltonian Systems

Kawano, Yu; Scherpen, Jacquelien M. A.

doi:10.1109/tac.2018.2811787

Cited by 10 publications

(8 citation statements)

References 20 publications

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“…A trivial solution to this problem takes place when Q or P coincides with the (scaled) Hamiltonian matrix H or its inverse. This idea was studied in [9] and [14], among other works; and for the sake of completeness, the following proposition identifies a class of CTLTI PH systems, for which the (scaled) Hamiltonian matrix, or its inverse, solves the inequalities (2) and (3).…”

Section: B Generalized Balancing Of Ctlti Ph Systemsmentioning

confidence: 99%

“…Moreover, the interconnection of two or more PH systems yields another PH system, which makes this modeling approach ideal to deal with large networks of physical systems. Some works where the problem of model reduction related to balancing of PH systems has been studied are [19] for LTI systems and [9] and [14] for the nonlinear case. With respect to those works, the novelty of this article lies in the use of extended balanced truncation to obtain the reduced-order model and, in contrast to the mentioned works, to establish an error bound.…”

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confidence: 99%

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Extended Balancing of Continuous LTI Systems: A Structure-Preserving Approach

Borja

Scherpen

Fujimoto

2023

IEEE Trans. Automat. Contr.

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In this article, we treat extended balancing for continuous-time linear time-invariant systems. We take a dissipativity perspective, thus, resulting in a characterization in terms of linear matrix inequalities. This perspective is useful for determining a priori error bounds. In addition, we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reducedorder model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model. We illustrate the results with a large-scale mechanical system example. Furthermore, we show how to interpret a reduced-order model of an electrical circuit again as a lower dimensional electrical circuit.

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Section: B Generalized Balancing Of Ctlti Ph Systemsmentioning

confidence: 99%

mentioning

confidence: 99%

Extended Balancing of Continuous LTI Systems: A Structure-Preserving Approach

Borja

Scherpen

Fujimoto

2023

IEEE Trans. Automat. Contr.

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“…Remark 8.2. MOR for pHODEs is discussed for instance in [4,5,23,37,38,40,45,58,71,81,95,96,112,118,142,166,176,177,199,201,205,208,[231][232][233]. Let us emphasize that for LTI systems, any passive system can be recast as a pH system, see [24,25].…”

Section: Example 81 Consider the Implicit Ode Systemmentioning

confidence: 99%

Control of port-Hamiltonian differential-algebraic systems and applications

Mehrmann¹,

Unger²

2022

Preprint

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The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving interconnection, congruence transformations, and Galerkin projection. Moreover, stability and passivity properties are easily shown. Condensed forms under orthogonal transformations present easy analysis tools for existence, uniqueness, regularity, and numerical methods to check these properties.After recalling the concepts for general linear and nonlinear descriptor systems, we demonstrate that many difficulties that arise in general descriptor systems can be easily overcome within the port-Hamiltonian framework. The properties of port-Hamiltonian descriptor systems are analyzed, time-discretization, and numerical linear algebra techniques are discussed. Structure-preserving regularization procedures for descriptor systems are presented to make them suitable for simulation and control. Model reduction techniques that preserve the structure and stabilization and optimal control techniques are discussed.The properties of port-Hamiltonian descriptor systems and their use in modeling simulation and control methods are illustrated with several examples from different physical domains. The survey concludes with open problems and research topics that deserve further attention.

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“…A trivial solution to this problem takes place when Q or P coincides with the (scaled) Hamiltonian matrix H or its inverse. This idea has been studied in [8] and [13], among other works; and for the sake of completeness, the proposition below identifies a class of CTLTI PH systems for which the (scaled) Hamiltonian matrix, or its inverse, solves the inequalities (2) and (3). Proof.…”

Section: Theorem 4 ([15]mentioning

confidence: 99%

Extended balancing of continuous LTI systems: a structure-preserving approach

Borja¹,

Scherpen²,

Fujimoto³

2020

Preprint

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In this paper, we treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structurepreserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model.

show abstract

Structure Preserving Truncation of Nonlinear Port Hamiltonian Systems

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Cited by 10 publications

References 20 publications

Extended Balancing of Continuous LTI Systems: A Structure-Preserving Approach

Extended Balancing of Continuous LTI Systems: A Structure-Preserving Approach

Control of port-Hamiltonian differential-algebraic systems and applications

Extended balancing of continuous LTI systems: a structure-preserving approach

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