Which modelling of system identification is supportive, when equations representing the system dynamics is implicit?

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Thanigaivel Raja T 2016-9-7

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I wish to perform system identification to validate a model. I found these sources when searching for the methods:

Grey box modelling: when equations representing system dynamics are explicit. (<http://in.mathworks.com/help/ident/ug/supported-grey-box-models.html>)

Black box modelling: when equations describing system are unknown/indescribable.(<http://in.mathworks.com/help/ident/ug/black-box-modeling.html>)

Then when equations representing the system dynamics is implicit, which modelling to be used? Also my model contains return statements upon certain conditions to represent inadequacy of model to solve for the specific cases.

Example of the Model

for i=1:numeric value1(say 100)
    Solve implicit equations of ODE's describing system dynamics
    if condition1 > numeric value2   %check for model inadequacy%
       return
    end
end