Difference between revisions of "Emgr"

Revision as of 10:06, 24 July 2018

Synopsis

emgr - Empirical Gramian Framework (Version 5.4). 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

Application matrix for the empirical gramian framework

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

emgr overview

applicable to:

Linear + Nonlinear Control Systems
First + Second Order Control Systems
Parametrized | Parametric Systems
Time Invariant + Varying Systems
Discretized PDEs

and with sample code for:

Balanced Truncation and balancing related methods
Combined State and Parameter Reduction
Parameter Identification + Sensitivity Analysis
Parameter Reduction + Robust Reduction
Optimal Sensor + Actuator Placement
Decentralized Control
Nonlinearity Quantification

References

C. Himpe. "emgr - The Empirical Gramian Framework". Algorithms 11(7): 91, 2018.

C. Himpe, T. Leibner, S. Rave, J. Saak. "Fast Low-Rank Empirical Cross Gramians". In: Proceedings in Applied Mathematics and Mechanics, vol. 17(1): 841--842, 2017.

C. Himpe. "Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience". Westfälische Wilhelms Universität, Sierke Verlag Göttingen, 2017.

C. Himpe, M. Ohlberger. "A note on the cross Gramian for non-symmetric systems". System Science and Control Engineering 4(1): 199--208, 2016.

C. Himpe, M. Ohlberger. "The Empirical Cross Gramian for Parametrized Nonlinear Systems". Proceedings of the 8th Vienna International Conference on Mathematical Modelling 48(1): 727--728, 2015.

C. Himpe, M. Ohlberger. "Model Reduction for Complex Hyperbolic Networks". Proceedings of the European Control Conference 2014: 2739--2743, 2014.

C. Himpe, M. Ohlberger. "Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems". Mathematical Problems in Engineering, vol. 2014: 843869, 2014.

C. Himpe, M. Ohlberger. "A Unified Software Framework for Empirical Gramians". Journal of Mathematics 2013: 365909, 2013.

Links

Official website: http://gramian.de

Meta Information: INI code-metadata

Oberwolfach References on Mathematical Software: Entry

Contact

Christian Himpe

@@ Line 47: / Line 47: @@
 == References ==
-* [[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]]. "<span class="plainlinks">[https://doi.org/10.3390/a11070091 emgr - The Empirical Gramian Framework]</span>". Algorithms 11(7): 91, 2018.
-* [[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]], T. Leibner, S. Rave, J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201710388 Fast Low-Rank Empirical Cross Gramians]</span>". In: Proceedings in Applied Mathematics and Mechanics, vol. 17(1): 841--842, 2017.
-* [[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]]. "<span class="plainlinks">[https://doi.org/10.14626/9783868448818 Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience]</span>". Westfälische Wilhelms Universität, Sierke Verlag Göttingen, 2017.
-* [[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.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://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.
-* [[User:Himpe|C. Himpe]]. "<span class="plainlinks">[http://doi.org/10.14626/9783868448818 Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience]</span>". Westfälische Wilhelms Universität, Sierke Verlag Göttingen, 2017.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1016/j.ifacol.2015.05.163 The Empirical Cross Gramian for Parametrized Nonlinear Systems]</span>". Proceedings of the 8th Vienna International Conference on Mathematical Modelling 48(1): 727--728, 2015.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1109/ECC.2014.6862188 Model Reduction for Complex Hyperbolic Networks]</span>". Proceedings of the European Control Conference 2014: 2739--2743, 2014.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://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: 843869, 2014.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2013/365909 A Unified Software Framework for Empirical Gramians]</span>". Journal of Mathematics 2013: 365909, 2013.
-* [[User:Himpe|C. Himpe]], T. Leibner, S. Rave, J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201710388 Fast Low-Rank Empirical Cross Gramians]</span>". In: Proceedings in Applied Mathematics and Mechanics, vol. 17(1): 841--842, 2017.
 == Links ==