How can I represent the terminal constraint set with respect to the Stability condition with MPC(Model Predictive Control)?
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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,
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/203462/image.png)
if the prediction horizon in a problem is equal to Hp, then the terminal constraint should be:
x(Hp) ∈ ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/203463/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/203463/image.png)
where
is the termal constraint set, MPIS and it is a kind of Polyhedron and it has two matrices, A and b.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/203464/image.png)
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
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/203465/image.png)
A*
= b. Which one is the right approach???
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/203466/image.png)
please help me
Thanks in advance.
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