Emgr

Synopsis

emgr - Empirical Gramian Framework (Version 5.8). 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 (parameter controllability)
• Empirical Identifiability Gramian (parameter observability)
• Empirical Joint Gramian (parameter observability)

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

Meta Information

Code Meta Data

name:	Empirical Gramian Framework (emgr)
version:	5.8 (2020-05-01)
id:	10.5281/zenodo.3779889 (doi)
author:	Christian Himpe (0000-0003-2194-6754)
topic:	Science, Mathematics, Model Reduction
type:	Toolbox
license:	BSD-2-Clause (open-source)
repository:	https://github.com/gramian/emgr (git)
language:	Matlab
dependencies:	Octave >=5.2, Matlab >=2017b
systems:	Linux, Windows
website:	https://gramian.de
keywords:	Controllability, Observability, Cross Gramian, Model Reduction, Model Order Reduction

References

• S. Grundel, C. Himpe, J. Saak. "On Empirical System Gramians". Proceedings in Applied Mathematics and Mechanics, 19: e201900006, 2019.

• 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". Proceedings in Applied Mathematics and Mechanics, 17: 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". IFAC-PapersOnLine (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: 2739--2743, 2014.

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

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

Links

• Official website: https://gramian.de

• Oberwolfach References on Mathematical Software: Entry

• DSweb Dynamical Systems Software: Entry

Contact

Christian Himpe