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'''emgr''' encompasses seven types of gramians: |
'''emgr''' encompasses seven types of gramians: |
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| − | * Empirical Controllability Gramian |
+ | * Empirical [[:Wikipedia:Controllability_Gramian|Controllability Gramian]] |
| − | * Empirical Observability Gramian |
+ | * Empirical [[:Wikipedia:Observability_Gramian|Observability Gramian]] |
| − | * Empirical Cross Gramian |
+ | * Empirical [[:Wikipedia:Cross_Gramian|Cross Gramian]] |
* Empirical Approximate Cross Gramian |
* Empirical Approximate Cross Gramian |
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* Empirical Sensitivity Gramian |
* Empirical Sensitivity Gramian |
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* Linear + Nonlinear Systems |
* Linear + Nonlinear Systems |
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* First + Second Order Systems |
* First + Second Order Systems |
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| − | * Parametric Systems |
+ | * Parametrized | Parametric Systems |
and with sample implementations for: |
and with sample implementations for: |
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| − | * Balanced Truncation + Direct Trunction |
+ | * [[Balanced Truncation]] + Direct Trunction |
* Parameter Identification + Sensitivity Analysis |
* Parameter Identification + Sensitivity Analysis |
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| − | * Parameter Reduction |
+ | * Parameter Reduction + Robust Reduction |
* Combined State and Parameter Reduction |
* Combined State and Parameter Reduction |
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* (Bayesian) Inverse Problem Reduction |
* (Bayesian) Inverse Problem Reduction |
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| + | * Decentralized Control |
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| + | * Nonlinearity Quantification |
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== References == |
== References == |
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| − | * C. Himpe, M. Ohlberger. "<span class="plainlinks">[http://dx.doi.org/10.1155/2013/365909 A Unified Software Framework for Empirical Gramians]</span>". Journal of Mathematics, vol. 2013, 2013. |
+ | * [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[http://dx.doi.org/10.1155/2013/365909 A Unified Software Framework for Empirical Gramians]</span>". Hindawi Journal of Mathematics, vol. 2013:1-6, 2013. |
== Links == |
== Links == |
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| − | * http://gramian.de |
+ | * Official website: http://gramian.de |
== Contact == |
== Contact == |
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Revision as of 11:12, 25 April 2014
Synopsis
emgr - Empirical Gramian Framework. Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification or 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
- Empirical Approximate Cross Gramian
- Empirical Sensitivity Gramian
- Empirical Identifiability Gramian
- Empirical Joint Gramian
applicable to:
- Linear + Nonlinear Systems
- First + Second Order Systems
- Parametrized | Parametric Systems
and with sample implementations for:
- Balanced Truncation + Direct Trunction
- Parameter Identification + Sensitivity Analysis
- Parameter Reduction + Robust Reduction
- Combined State and Parameter Reduction
- (Bayesian) Inverse Problem Reduction
- Decentralized Control
- Nonlinearity Quantification
References
- C. Himpe, M. Ohlberger. "A Unified Software Framework for Empirical Gramians". Hindawi Journal of Mathematics, vol. 2013:1-6, 2013.
Links
- Official website: http://gramian.de