Fixed initial conditions: global identifiability

In addition to knowing the ODE system and time series data for some outputs, one frequently also knows the initial conditions for some of the states. It would be great to use this information to clarify the identifiability analysis.
For an algorithm based on input-output equations, an interesting discussion of this problem can be found in this paper. To the best of my understanding, the paper does not give a complete algorithm but some ideas can be of interest.

Some interesting specific things we could do:

• fixed initial conditions can be used when verifying the rank of the Wronskian. If it is still of full rank, then identifiability with these fixed initial conditions is at least as good as without them (that is, we do not loose identifiability because of hitting a singular point).
• As suggested in the paper mentioned above, if the system is controllable from the fixed initial conditions, then again the result is at least as good.
• What would be interesting to see is if we could get a different result of elimination by making some initial conditions fixed in the GenericPointGenerator used in the elimination process...

Start by reading the identifiability analysis and the GenericPointGenerator elimination process, then review the linked paper for the proposed treatment of fixed initial conditions. The work is done when the analysis can use specified fixed initial conditions and reports the resulting global identifiability behavior, including the Wronskian and controllability cases described in the issue.