Dynamical Systems Magazine

emgr - EMpirical GRamian Framework

By Christian Himpe
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In control and system theory the system Gramian matrices of linear input-output systems have wide-spread use, for example in: model reduction, decentralized control, optimal placement, sensitivity analysis or parameter identification. Empirical Gramian matrices correspond to the (linear) system Gramians, but extend to nonlinear systems, due to their data-driven computation. The empirical Gramian framework is an open-source Matlab toolbox, enabling the computation of the following empirical system Gramians:

Empirical System Gramians:

  • Empirical Controllability Gramian
  • Empirical Observability Gramian
  • Empirical Cross Gramian
  • Empirical Linear Cross Gramian
  • Empirical Sensitivity Gramian (Controllability of parameters)
  • Empirical Identifibility Gramian (Observability of parameters)
  • Empirical Joint Gramian (Minimality of state and observability of parameters)

Features:

  • Interfaces for: Custom solvers and inner product kernels
  • Non-Symmetric option for all cross Gramians
  • Compatible with OCTAVE, MATLAB and PYTHON (experimental)
  • Vectorized
  • Shared and distributed memory parallelizable
  • Functional
  • Open-source

More Information: https://gramian.de


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Combined state and parameter reducibility for a nonlinear transport problem with local velocity parametrization.

KeywordsMatlab, Octave, Gramian, Controllability, Observability
Model
  • ODEs
  • Other
Software Type
  • Package
Language
  • MatLab
  • Python
Platform
  • Linux
  • Windows
Availability
Contact Person
References to Papers
C. Himpe. emgr - The Empirical Gramian Framework. Algorithms 11(7): 91, 2018. doi:10.3390/a11070091.
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