Maximum MPC prediction horizon for an unstable plant

Question

In the following book,

Model Predictive Control ToolboxTM (User's Guide)

    Alberto Bemporad
    Manfred Morari
    N. Lawrence Ricker

At page 1-6, it has been mentioned that

If the plant is open-loop unstable, the maximum possible p is the number of control intervals required for the plant’s open-loop step response to become infinite.

Here, p means the prediction horizon.

This claim does not look reasonable to me. I have not understood the reason for this claim. What will happen if I choose the prediction horizon longer?

Answer 1

I think the book is using "infinite" to mean "a number that is too big for the computer software to represent", not in the strict mathematical sense. See near the top of page 1-6:

Open-loop unstable plants: if p*Ts is too large, such that the plant step responses become infinite during this amount of time, key parameters needed for MPC calculations become undefined, generating an error message.

So, this is practical limitation of how the software works, not a theoretical limitation of the MPC method.