Changing constraints and bounds on slack variables

pihka · March 19, 2025, 10:48pm

Hi

I am currently using acados for a MPC formulation. In my formulation I want to alter the bounds on my slack variables. I am using acados in Python3.

My system is in discrete time.

For example, I predict 40 time steps, and in time steps 20-25, I want to set the bounds on my slack variables to 0, in all other time steps, I set them to a fixed value, say, 10^6.
Is this possible in acados?

In the documentation there is the api constraints_set, but this does not allow to set the bounds of the slack variables, for example ush.

kaethe · March 20, 2025, 6:35am

Hi

Just to clarify: are you trying to switch between hard constraints (slack needs to be zero) and soft constraint (slack can take any positive value)?

Best, Katrin

pihka · March 20, 2025, 8:08am

Hi Katrin,

Thank you for the swift reply.

Yes, that is what I want to do. I want for some stages the nonlinear constraint h to be a soft constraint while for some other stages to be a hard constraint.

Kind regards,
Peter Karstensen

kaethe · March 20, 2025, 8:45am

Hi Peter, this can be implemented via a multi-phase formulation. The main idea is to specify multiple OCPs, one for each phase, and specify which shooting nodes belong to which phase. In your example, you will need three phases, node 1 to 19, node 20 to 25, node 26 to 40.

Here is an example that illustrates how to formulate MOCPs:

github.com/acados/acados

examples/acados_python/multiphase_nonlinear_constraints/main.py

main

# -*- coding: future_fstrings -*-
#
# Copyright (c) The acados authors.
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# This file is part of acados.
#
# The 2-Clause BSD License
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
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# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

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and here’s our recent publication introducing MOCPs in acados.

Best, Katrin