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