Balanced truncation model reduction for systems with inhomogeneous initial conditions

Heinkenschloss, Matthias; Reis, Timo; Antoulas, Athanasios C.

doi:10.1016/j.automatica.2010.12.002

Cited by 64 publications

(82 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When the initial condition is nonzero but known, this information could be easily included in the time-domain POD method as the initial condition for the numerical simulation. For rational interpolation and balanced truncation approaches, the nonzero initial conditions can be appended to the input-state-matrix B(p) representing an initial impulse as done in [30,57,128]. However, if the initial condition is unknown and/or the reduced model needs to provide a good approximation for a wide range of initial conditions, the corresponding model reduction problem can no longer be easily handled by simple modification of the zero-initial condition case.…”

Section: 7mentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

View full text Add to dashboard Cite

Abstract. Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for which the equations governing the system behavior depend on a set of parameters. Examples include parameterized partial differential equations and large-scale systems of parameterized ordinary differential equations. The goal of parametric model reduction is to generate low-cost but accurate models that characterize system response for different values of the parameters. This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lends insights to potential advantages and disadvantages in applying each of the methods. We highlight the important role played by parametric model reduction in design, control, optimization, and uncertainty quantification-settings that require repeated model evaluations over different parameter values.

show abstract

Section: 7mentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

View full text Add to dashboard Cite

show abstract

“…In [112], an extension of the standard balanced truncation method to systems with inhomogeneous initial conditions is presented and error estimates were given. We propose a slightly different approach and derive an error bound at the end of this section.…”

Section: Error Bound For Systems With Nonzero Initial Conditionsmentioning

confidence: 99%

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

Baur

Benner

Feng

2014

Arch Computat Methods Eng

294

270

View full text Add to dashboard Cite

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.

show abstract

“…Quite successful methods have been implemented, including but not limited to: balancedtruncation algorithms, see e.g. [5], Moment matching techniques [3], projection-based procedures, optimal and convexoptimization techniques, see e.g., [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

“…H 2 -norm minimization-based algorithms [11], convex-optimization-based techniques [10,9,12,], and Hankel model-reduction-based procedures [13] have shown their good performances for a variety of dynamical systems. The reader is also referred to the references [14][15][16]3,17,5,18] for different looks on model reduction using Kalman's minimal realization and balanced truncation procedures. Recent optimization techniques as numerical genetic algorithms and Particle Swarm Optimizationbased procedures have been successfully applied to model reduction and identification, see e.g., [19] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Model reduction of a class of discrete-time nonlinear systems

Ibrir

Bettayeb

2015

Applied Mathematics and Computation

View full text Add to dashboard Cite

Balanced truncation model reduction for systems with inhomogeneous initial conditions

Cited by 64 publications

References 7 publications

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

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

Model reduction of a class of discrete-time nonlinear systems

Contact Info

Product

Resources

About