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.