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EPiC Series in Computing Large-Scale Linear Systems from Order-Reduction (Benchmark Proposal)

Hoang-Dung Tran, Viet Luan, Taylor Nguyen, Johnson
ARCH16 (EPiC Series in Computing   unpublished
This benchmark suite is composed of nine examples of large-scale linear systems, ranging in di-mensionality in the tens to the low thousands.  ...  order reduction [11, 12].  ...  order reduction [11, 12] .  ... 

A mathematical biography of Danny C. Sorensen

Peter Benner, Mark Embree, Richard B. Lehoucq, C.T. Kelley
2012 Linear Algebra and its Applications  
On the occasion of his 65th birthday, we briefly recount Dan Sorensen's profound contributions to optimization, numerical linear algebra, and model order reduction for dynamical systems.  ...  This work on large-scale eigenvalue computations naturally dovetailed into Dan's later work on Krylov subspace techniques for model reduction of large-scale dynamical systems.  ...  to Krylov subspace-based MOR methods for large-scale systems.  ... 
doi:10.1016/j.laa.2012.01.031 fatcat:hm3b7fqamvcxjphqletg7ze7va

Dynamic model reduction: An overview of available techniques with application to power systems

Savo Djukic, Andrija Saric
2012 Serbian Journal of Electrical Engineering  
This paper summarises the model reduction techniques used for the reduction of large-scale linear and nonlinear dynamic models, described by the differential and algebraic equations that are commonly used  ...  Part of the paper is devoted to the techniques commonly used for reduction (equivalencing) of large-scale power systems, which are based on coherency, synchrony, singular perturbation analysis, modal analysis  ...  In [4] a method that combines POD (see Subsection 4.1) and concepts from balanced realization theory, for performing a reduction of a large-scale linear system is presented.  ... 
doi:10.2298/sjee1202131d fatcat:k2nqxgyb4ralbedtzcovghfhyq

Cross-Gramian-Based Combined State and Parameter Reduction for Large-Scale Control Systems

Christian Himpe, Mario Ohlberger
2014 Mathematical Problems in Engineering  
The joint gramian allows not only a reduction of the parameter space but also the combined state and parameter space reduction, which is tested on a linear and a nonlinear control system.  ...  This work also introduces the empirical joint gramian, which is derived from the empirical cross-gramian.  ...  Introduction The evaluation of large-scale dynamical systems, which arise, for example, from complex networks or discretized partial differential equations, may require model reduction due to limitations  ... 
doi:10.1155/2014/843869 fatcat:cf7po3xovrfnzm4ahs272btqqa

Order Reduction of Parametrically Excited Nonlinear Systems: Techniques and Applications

2005 Nonlinear dynamics  
Here the system is converted into an equivalent second order nonlinear system with time invariant linear system matrices and periodically modulated nonlinearities via the L-F and other canonical transformations  ...  The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered in state space and in direct second order (structural) form.  ...  Reduced order models constructed from this method capture the dynamics of original large-scale system more accurately than other approaches.  ... 
doi:10.1007/s11071-005-2822-z fatcat:fcbvym4uszdqbdogdvu5xdjtha

Pole placement and order reduction in two-time-scale control systems through Riccati iteration

Leonard R. Anderson
1982 Mathematical Modelling  
A transformation of variables taken from singular perturbations may be applied to two-time-scale linear systems in state space form to reduce the system to block-diagonal form with slow and fast modes  ...  Provided the fast subsystem is stable, the order reduction can be expected to yield a good approximation to the original system.  ...  As noted above, order reduction is often required in the study of large scale systems, and this may be conveniently done using decoupled subsystems (13a, b).  ... 
doi:10.1016/0270-0255(82)90015-x fatcat:sk5keywoqbaufcnihkregc5xm4

Parametric Model Order Reduction of Port-Hamiltonian Systems by Matrix Interpolation

Markus Giftthaler, Thomas Wolf, Heiko K. F. Panzer, Boris Lohmann
2014 at - Automatisierungstechnik  
In this paper, parametric model order reduction of linear time-invariant systems by matrix interpolation is adapted to large-scale systems in port-Hamiltonian form.  ...  A new weighted matrix interpolation of locally reduced models is introduced in order to preserve the port-Hamiltonian structure, which guarantees the passivity and stability of the interpolated system.  ...  In this paper, the framework for parametric model order reduction of linear time-invariant systems as presented by Panzer et al. in [5] is extended to linear timeinvariant (LTI) systems that are originally  ... 
doi:10.1515/auto-2013-1072 fatcat:x64mbvxqdnfoxcgnpo2sblvw2e

Efficient State Estimation for Gas Pipeline Networks via Low-Rank Approximations [article]

Nadine Stahl, Nicole Marheineke
2021 arXiv   pre-print
For large-scale gas pipeline networks structure-preserving model order reduction has turned out to be an advantageous way to compute accurate solutions with much less computational effort.  ...  The matrix evaluations become memory-intensive and expensive for large-scale systems. Establishing a model hierarchy, we derive a low-rank approximation from projectionbased model order reduction.  ...  Gas network models are large-scale systems of high complexity.  ... 
arXiv:2007.15988v2 fatcat:lc5dba6dwfd5vem7dwdwwdq54u

Model Order Reduction and Linear Quadratic Regulator Controller Design on A Large Scale Linear Time Invariant System

N. V. A. Ravikumar et al., N. V. A. Ravikumar et al.,
2017 International Journal of Mechanical and Production Engineering Research and Development  
The main objective of this paper, aims to apply model order reduction on a large scale system and design a Linear Quadratic Regulator (LQR) based controller, to analyse the performance indices, in the  ...  The order of the designed controller must be close to the order of the large scale system, or even more in most cases.  ...  One of the most important properties employed in model order reduction is to retain the predominant characteristics of the large scale system.  ... 
doi:10.24247/ijmperddec201761 fatcat:7w3dklg43fg7rbb72oisreef64

Reduction of Protein Networks Models by Passivity Preserving Projection

Luca Mesin, Flavio Canavero, Lamberto Rondoni
2013 Communications in Theoretical Physics  
The reduction method does not require to solve the complete system, resulting in a promising tool for studying very large-scale models for which the full solution cannot be computed.  ...  Keeping constant the reduction factor, the approximation error is lower for larger systems.  ...  of large systems (reduction factor of the order of 70-80%, for systems of at least 60 equations).  ... 
doi:10.1088/0253-6102/60/2/18 fatcat:fnkw2frsdvdy3lsqlnbxptykqq

Off-line model reduction for on-line linear MPC of nonlinear large-scale distributed systems

Weiguo Xie, Ioannis Bonis, Constantinos Theodoropoulos
2011 Computers and Chemical Engineering  
from the large-scale ones.  ...  To overcome the excessive computational cost of MPC application for large-scale nonlinear systems, model reduction methodology in conjunction with efficient system linearizations have been exploited to  ...  The main purpose of this work is to combine an off-line model reduction technique, namely the POD method, with linear MPC for nonlinear large-scale systems.  ... 
doi:10.1016/j.compchemeng.2011.01.023 fatcat:qqnpcp4qrbdbrdeltll66m2k34

Parallel Implementation of LQG Balanced Truncation for Large-Scale Systems [chapter]

Jose M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, Alfredo Remón
2008 Lecture Notes in Computer Science  
Model reduction of large-scale linear time-invariant systems is an ubiquitous task in control and simulation of complex dynamical processes.  ...  We discuss how LQG balanced truncation can be applied to reduce the order of large-scale control problems arising from the spatial discretization of time-dependent partial differential equations.  ...  Concluding Remarks We have provided evidence in support of the benefits of the LQG BT method for model reduction of large-scale systems.  ... 
doi:10.1007/978-3-540-78827-0_24 fatcat:uzmymuxsmfdulgk64xswpty3we

A note on model reduction of large scale systems

O Ibidapo-Obe
1982 Journal of Mathematical Analysis and Applications  
INTRODUCTION In an earlier paper [ 11, results on model reduction of large scale systems were given using a multivariate linear regression scheme.  ...  (2) In model reduction, it is desirable to find an mth-order system S, described by S,:i=Fz+Gu.  ... 
doi:10.1016/0022-247x(82)90075-0 fatcat:ird6yctzurhulfyqtb4yehyj4q

Combined Reduction

Christian Himpe, Mario Ohlberger
2014 Zenodo  
presented at Model Reduction and Approximation for Complex Systems - june 2013  ...  Example Large-Scale Nonlinear System Σ 1 = ẋ = A tanh(x) + Bu y = Cx • 16 Extreme-Scale Linear System Σ 2 = ẋ = Ax + Bu y = Cx • 256 Full order optimization duration compared to offline and online  ...  framework (emgr) • Lengthy offline times greedy comred.m • (Currently only) Linear systems • Non-symmetric and non-square systems • Enables extreme-scale system reduction • No dependencies • Very  ... 
doi:10.5281/zenodo.8624 fatcat:2pbk3h3blvbgvoyfavigf6iafu

Model reduction for linear parameter varying systems using scaled diagonal dominance

Harald Pfifer, Tamas Peni
2016 2016 American Control Conference (ACC)  
A model-reduction method for linear, parametervarying (LPV) systems based on parameter-varying balanced realizations is proposed.  ...  Since the scalability of SOCP solvers is much better than that of the SDPs, the new formulation allows solving large scale model reduction problems more efficiently.  ...  NNX12AM55A entitled "Analytical Validation Tools for Safety Critical Systems Under Loss-of-Control Conditions" Dr. Christine Belcastro is the technical monitor.  ... 
doi:10.1109/acc.2016.7525344 dblp:conf/amcc/PfiferP16 fatcat:dzoediylynbs3bt7mo5lqs4zby
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