FIRST, READ THE LICENSE AT THE END OF THIS FILE
A detailed post accompanying the codes can be found on this webpage: https://aleksandarhaber.com/introduction-to-subspace-system-identification-system-identification-tutorial/
Briefly speaking, the coded subspace identification method estimates a state-space model
x_{k+1}=Ax_{k}+Bu_{k}
y_{k}=Cx_{k}
or the Kalman innovation state space model
x_{k+1}=Ax_{k}+Bu_{k}+Ke_{k}
y_{k}=Cx_{k}+e_{k}
using only the input-output data sequences (u_{k},y_{k}) for k=0,1,2,..., N. Also, the method can estimate the model order.
I have implemented a version of the Predictor Based Subspace IDentification (PBSID) method. The description of the algorithm can be found in the following papers:
A. Haber, Subspace Identification of Temperature Dynamics, https://arxiv.org/abs/1908.02379 https://arxiv.org/abs/1908.02379
If you want to refer to this implementation in your paper or report, cite that paper and this GitHub repository. Explanation of the files:
"test_subspace.py" - is a driver code for testing the subspace identification method, you should start from here.
"discretization_test.py" - is used to test the backward Euler method for discretizing a dynamical system
"functionsSID.py" - contains the functions used to estimate the model, the functions from this file are imported in "test_subspace.py"
All the questions and comments should be addressed to me:
Aleksandar Haber aleksandar.haber@gmail.com
Also, if you are interested in improving the codes, please let me know. This implementation is not optimized for large-scale problems.
LICENSE: THIS IS NOT FREE SOFTWARE AND CODE. IF YOU WANT TO USE THIS CODE IN THE COMMERCIAL SETTING OR ACADEMIC SETTING, THAT IS, IF YOU WORK FOR A COMPANY OR IF YOU ARE AN INDEPENDENT CONSULTANT AND IF YOU WANT TO USE THIS CODE OR IF YOU ARE ACADEMIC RESEARCHER OR STUDENT, THEN WITHOUT MY PERMISSION AND WITHOUT PAYING THE PROPER FEE, YOU ARE NOT ALLOWED TO USE THIS CODE. YOU CAN CONTACT ME AT
TO INFORM YOURSELF ABOUT THE LICENSE OPTIONS AND FEES FOR USING THIS CODE. ALSO, IT IS NOT ALLOWED TO
(1) MODIFY THIS CODE IN ANY WAY WITHOUT MY PERMISSION.
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DELIBERATE OR INDELIBERATE VIOLATIONS OF THIS LICENSE WILL INDUCE LEGAL ACTIONS AND LAWSUITS.