How can I add contraints to a model ( non linear arx, arx, armax ...) ?

Hello,

I have a set of data which describes a temperature process. The dataset contains various temperatures from sensors and

the voltage input. I already estimated several models from the data, but I wondered if it is possible to add contraints

when I create the models? For example I would like to state that the minimum Temperature for all sensors is 25 degrees (since

that is room temperature). Is it possible to include that information to may model somehow?

Answer 1

[Rajiv Singh]

If the constraints can be expressed as lower or upper bounds on the model's parameters, the estimations routines will handle them. The process looks like:

1. Create model template, e.g., sys = idss(...)
2. Specify bounds on parameters; sys.Structure.<parameter>.Minimum = ...
3. Identify the structured model: sys2 = <estimator>(data, sys)

For more complex constraints, such as parameter inter-relationships, you need to use the grey box modeling approach. See:

https://www.mathworks.com/help/ident/ug/estimating-coefficients-of-odes-to-fit-given-solution.html

https://www.mathworks.com/help/ident/ug/estimate-complex-conjugate-poles-and-zeros-using-grey-box-model.html

Answer 2

[Nils B]

Thanks for your answer, however your approach is not possible with non liniar ARX models, since they don't provide a property like idss models. Do you know a way to solve that, beside the grey model approach because the differntial equations of the system are not known?