A greedy rational Krylov method for &amp;#x210B;&lt;inf&gt;2&lt;/inf&gt;-pseudooptimal model order reduction with preservation of stability

Panzer, Heiko K. F.; Jaensch, S.; Wolf, Thomas; Lohmann, Boris

doi:10.1109/acc.2013.6580700

Cited by 19 publications

(29 citation statements)

References 6 publications

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“…The SPARK algorithm in [151] is an iterative scheme to adaptively chose the expansion points in Krylov subspace methods, and in particular the order of the reduced model. It implicitly guarantees preservation of stability and contains an optimization algorithm that converges to an H 2 optimum.…”

Section: Recent Progresses On the Above Issuesmentioning

confidence: 99%

Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective

Baur

Benner

Feng

2014

Arch Computat Methods Eng

294

270

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In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and wide applicability for simulating large-scale mathematical models in engineering and the sciences. Recently, MOR has been intensively further developed for increasingly complex dynamical systems. Wide applications of MOR have been found not only in simulation, but also in optimization and control. In this survey paper, we review some popular MOR methods for linear and nonlinear large-scale dynamical systems, mainly used in electrical and control engineering, in computational electromagnetics, as well as in micro-and nanoelectro-mechanical systems design. This complements recent surveys on generating reduced-order models for parameterdependent problems (Benner et al. in 2013; Boyaval et al. in Arch Comput Methods Eng 17(4):435-454, 2010; Rozza et al. Arch Comput Methods Eng 15(3):229-275, 2008) which we do not consider here. Besides reviewing existing methods and the computational techniques needed to implement them, open issues are discussed, and some new results are proposed.

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Section: Recent Progresses On the Above Issuesmentioning

confidence: 99%

Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective

Baur

Benner

Feng

2014

Arch Computat Methods Eng

294

270

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“…In [7,22] Gugercin et al proposed an Iterative Rational Krylov Algorithm (IRKA) to compute a reduced order model satisfying the firstorder conditions for the H 2 approximation. Other adaptive methods (for the SISO case) are introduced in [9,19,20,25,27,30] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Rational Block Lanczos-Type Algorithm for Model Reduction of Large Scale Dynamical Systems

2015

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Mathematical modeling of complex electrical systems, has led us to linear mathematical models of higher order. Consequently, it is difficult to analyse and to design a control strategy of these systems. The order reduction is an important and effective tool to facilitate the handling and designing of a control strategy. In this paper we present, firstly, a reduction method which is based on the Krylov subspace and Lyapunov techniques, that we call Lyapunov-Global-Lanczos. This method minimizes the H∞ norm error, absolute error and preserves the stability of the reduced system. It also provides a better reduced system of order 1, with closer behaviour to the original system. This first order system is used to design PI (Proportional-Integral) controller. Secondly, we implement an adaptive digital PI controller in a microcontroller. It calculates the PI parameters in real time, referring to the error between the desired and measured outputs and the initial values of PI controller, that were determined from the first order system. Two simulation examples and a real time experimentation are presented to show the effectiveness of the proposed algorithms.

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“…AN ADAPTIVE FRAMEWORK In this contribution, we present the current developments on the adaptive selection of a) the reduced order n and b) the position of the shifts s 0 , both introduced by Panzer et al (2013a). The cornerstone of the discussion is given by an unconventional representation of the error system G e (s).…”

mentioning

confidence: 99%

“…Assuming asymptotic stability of the HFM, the choice of shifts can be parametrized by two positive real numbers and a greedy, trust-region based algorithm for the detection of locally H 2 -optimal shifts can be implemented, bypassing the convergence issues related to IRKA. This algorithm was first introduced by Panzer et al (2013a) under the name of Stability Preserving Adaptive Rational Krylov (SPARK). It can be shown that in H 2 -pseudo-optimal reduction, the minimization of the H 2 -norm of the error system (3) corresponds to the maximization of the H 2 -norm of the ROM, yielding a cheap cost functional for SPARK.…”

mentioning

confidence: 99%

Advances on the Adaptive Selection of Both Shifts and Reduced Order in H2 -Pseudo-Optimal Model Reduction

et al. 2015

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A greedy rational Krylov method for ℋ<inf>2</inf>-pseudooptimal model order reduction with preservation of stability

Cited by 19 publications

References 6 publications

Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective

Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective

An Adaptive Rational Block Lanczos-Type Algorithm for Model Reduction of Large Scale Dynamical Systems

Advances on the Adaptive Selection of Both Shifts and Reduced Order in H2 -Pseudo-Optimal Model Reduction

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