Include both satge and terminal slack variables in stage cost and stage constraints

User Questions
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1

Hi everyone,
I am currently trying to implement such a OCP formulation with soft constraints as in the paper:
Soft Constrained Model Predictive Control With Robust Stability Guarantees from Melanie N. Zeilinger et.al (Soft Constrained Model Predictive Control With Robust Stability Guarantees | IEEE Journals & Magazine | IEEE Xplore)

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As the photo above right side, we have in stage cost for slack variable and in stage constraints such terms, in which both stage slack epsilon_i and terminal slack epsilon_s exist.

However, in acados problem formulation, as the left side, we can’t add a term related to terminal slack variable to stage cost or any stage constraint.

Is there a way to implement this kind of formulation with acados? Or it is not supported now?

Thank you very much in advance!
Yiwei Wang

2

Yes you can, see the “terminal constraints” part of the problem formulation PDF.

3

Hello,thanks for you replay. However I am still not clear after reading the PDF.
For example: here we can map terminal slacks on to the constraint for x(T) , which is terminal constraint for state variable. But what I need to implement is to map terminal slacks on to the constraint for x(t) , which is path constraint.

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Or if we look at all the path constraints directly, we can not see any terminal slack variables like s^e_{…}
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Could you please specify why it should be possible?
Thank you!
Yiwei

4

@yiweiwang
Hi, yiwen Wang,
Have you already applied slack variables in ACADOS? I am currently facing the same problem as you, how to add slack variables and their cost function. If possible, could you also provide me with some guidance? Thank you advanced.