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* Empirical [[:Wikipedia:Controllability_Gramian|Controllability Gramian]] |
* Empirical [[:Wikipedia:Controllability_Gramian|Controllability Gramian]] |
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* Empirical [[:Wikipedia:Observability_Gramian|Observability Gramian]] |
* Empirical [[:Wikipedia:Observability_Gramian|Observability Gramian]] |
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| − | * Empirical [[:Wikipedia:Cross_Gramian|Cross Gramian]] |
+ | * Empirical [[:Wikipedia:Cross_Gramian|Cross Gramian]] (including an Empirical Non-Symmetric Cross Gramian) |
* Empirical Linear Cross Gramian |
* Empirical Linear Cross Gramian |
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* Empirical Sensitivity Gramian |
* Empirical Sensitivity Gramian |
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* Discretized [[:Wikipedia:Partial_differential_equation|PDEs]] |
* Discretized [[:Wikipedia:Partial_differential_equation|PDEs]] |
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| − | and with sample |
+ | and with sample code for: |
* [[Balanced Truncation]] + Direct Trunction |
* [[Balanced Truncation]] + Direct Trunction |
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* Parameter Reduction + Robust Reduction |
* Parameter Reduction + Robust Reduction |
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* Combined State and Parameter Reduction |
* Combined State and Parameter Reduction |
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| − | * Uncertainty Quantification |
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* Decentralized Control |
* Decentralized Control |
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* Nonlinearity Quantification |
* Nonlinearity Quantification |
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Revision as of 14:08, 3 March 2015
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 (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
- 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.
Links
- Official website: http://gramian.de
- Meta Information: code.jsonld , code.xml