How to do parameter estimation of a ODE based model?

Original question

I would like to do parameter estimation of a ODE based model, does anyone have some clues how to do it in MATLAB?

Follow-up question

Does anyone know a good way to merge MATLAB with Python so that I do not need to switch back and forth?

[Arkadiy Turevskiy]

You should not be editing your questions like you did. You should post a new question instead, and leave the old one in place. With the edits you did to the question, the provided answers no longer make sense.

[Cedric]

I'll answer in your new thread when you'll have started it.

[Randy Souza]

I have restored the original text of this question.

Tongli, as Arkadiy and Cedric pointed out, please ask a new question so that the answers to this one continue to make sense. Also, if one of the answers helped solve your problem, please vote for and/or accept the best answer.

Answer 1

[Arkadiy Turevskiy]

There are actually many ways you could do it:

1. Implement your model, write a cost function, and use Optimization Toolbox to minimize this cost function by fitting parameters to have model output match the data.

2. Use gray-box system identification capabilities of System Identification Toolbox. See examples in the section called Nonlinear Grey-Box Model Identification on this page.

3. Implement your model in Simulink and use Simulink Design Optimization. See the short demo here.

Many of these options are explained in more detail in the parameter estimation page.

HTH.

Arkadiy

[Rajiv Singh]

In particular, see: http://www.mathworks.com/help/ident/ug/estimating-coefficients-of-odes-to-fit-given-solution.html

Answer 2

[Babak]

There are lessons on how to design an observer for a system in controls theory.

They use the output of the estimator as the input to the controller.

Please google, "observer design" to find links on how to do it.

The observer is to estimate the states of the system which is made up of ODEs.