Parameter Estimation of Time Varying State

I have a state space grey box model for which I have been using the PEM tool to determine one term in the state matrix for a given set of test data. The limiation I am finding with using the PEM tool is that the state has to be constant throughout the entire set of test data. I am looking for a way to determine the state as a function of time (the state is actually dependent on several other known factors). In the end, I am looking to determine the state vs. time so that I can generate a lookup table for the state as a function of the other known inputs.

Answer 1

[Rajiv Singh]

Do you mean that the state-space matrices A,B,C,D are time dependent? If so, please look into the "nonlinear grey box" modeling technique:

http://www.mathworks.com/help/toolbox/ident/ug/bqs6lf8.html

In: http://www.mathworks.com/products/sysid/demos.html,

see: "Tutorials on Nonlinear Grey Box Model Identification"

Unlike the linear grey box (idgrey) case, the ODE function of a nonlinear grey box model (idnlgrey) takes in the current time instant t, input u(t) and state value x(t) as regular input arguments. Hence you can create a dependency of parameters on time values.

[Ahmad Gad]

Can you explain this more? None of the links work.