How can I represent the terminal constraint set with respect to the Stability condition with MPC(Model Predictive Control)?

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Kim MinSung 2019-2-10

Some people in here may know an approach for guanteeing the recursive feasibility and stability with Model Predictive Ctonrol(MPC).

So, May I give a question in here about that?

To consider the recursive feasibility and statbility in MPC, there are two methods.

First one is making a Lyapunov Function about the terminal penalty cost function and

another one is making a terminal constraint set of Maximal Positive Invariant Set(MPIS)

Ok. In a short what I want to know is just like this:

There is a terminal constraint set,

if the prediction horizon in a problem is equal to Hp, then the terminal constraint should be:

x(Hp) ∈

where

is the termal constraint set, MPIS and it is a kind of Polyhedron and it has two matrices, A and b.

And, the main question is here... How can I use this term at the implenmenting step? The two matrices mentioned above, A and b.

A *

(x state at the terminal ) <= b or

= b. Which one is the right approach???

please help me

Thanks in advance.

Min

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