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== Synopsis == |
== Synopsis == |
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| − | [http://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework (Version |
+ | [http://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework (Version 5.0). |
Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification. |
Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification. |
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Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction. |
Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction. |
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* First + Second Order Control Systems |
* First + Second Order Control Systems |
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* Parametrized | Parametric Systems |
* Parametrized | Parametric Systems |
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| + | * Time Inavriant + Varying Systems |
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* Discretized [[:Wikipedia:Partial_differential_equation|PDEs]] |
* Discretized [[:Wikipedia:Partial_differential_equation|PDEs]] |
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== References == |
== References == |
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| − | * [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[http:// |
+ | * [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[http://doi.org/10.1155/2013/365909 A Unified Software Framework for Empirical Gramians]</span>". Journal of Mathematics, vol. 2013:1--6, 2013. |
| − | * [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[http:// |
+ | * [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[http://doi.org/10.1155/2014/843869 Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems]</span>". Mathematical Problems in Engineering, vol. 2014:1--13, 2014. |
| − | * [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[http:// |
+ | * [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[http://doi.org/10.1109/ECC.2014.6862188 Model Reduction for Complex Hyperbolic Networks]</span>". Proceedings of the ECC'14: 2739--2743, 2014. |
| + | |||
| + | * [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[http://doi.org/10.1080/21642583.2016.1215273 A note on the cross gramian for non-symmetric systems]</span>". System Science and Control Engineering 4(1): 199--208, 2016. |
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== Links == |
== Links == |
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Revision as of 14:57, 20 October 2016
Synopsis
emgr - Empirical Gramian Framework (Version 5.0). Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification. Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction. The emgr framework is a compact open source toolbox for gramian-based model reduction and compatible with OCTAVE and MATLAB.
Features
emgr encompasses seven types of gramians:
- Empirical Controllability Gramian
- Empirical Observability Gramian
- Empirical Cross Gramian (including an Empirical Non-Symmetric Cross Gramian)
- Empirical Linear Cross Gramian
- Empirical Sensitivity Gramian
- Empirical Identifiability Gramian
- Empirical Joint Gramian
applicable to:
- Linear + Nonlinear Control Systems
- First + Second Order Control Systems
- Parametrized | Parametric Systems
- Time Inavriant + Varying Systems
- Discretized PDEs
and with sample code for:
- Balanced Truncation + Direct Trunction
- Parameter Identification + Sensitivity Analysis
- Parameter Reduction + Robust Reduction
- Combined State and Parameter Reduction
- Decentralized Control
- Nonlinearity Quantification
References
- C. Himpe, M. Ohlberger. "A Unified Software Framework for Empirical Gramians". Journal of Mathematics, vol. 2013:1--6, 2013.
- C. Himpe, M. Ohlberger. "Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems". Mathematical Problems in Engineering, vol. 2014:1--13, 2014.
- C. Himpe, M. Ohlberger. "Model Reduction for Complex Hyperbolic Networks". Proceedings of the ECC'14: 2739--2743, 2014.
- C. Himpe, M. Ohlberger. "A note on the cross gramian for non-symmetric systems". System Science and Control Engineering 4(1): 199--208, 2016.
Links
- Official website: http://gramian.de
- Meta Information: INI code-metadata
- Oberwolfach References on Mathematical Software: Entry