# ~~~
# This file is part of the paper:
#
#           " Be greedy and learn: efficient and certified algorithms
#                    for parametrized optimal control problems "
#
#   https://github.com/HenKlei/ML-OPT-CONTROL.git
#
# Copyright 2023 all developers. All rights reserved.
# License: Licensed as BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
# Authors:
#   Hendrik Kleikamp, Martin Lazar, Cesare Molinari
# ~~~

Optimal control of parametrized linear systems using machine learning

In this repository, we provide the code used for the numerical experiments in our paper "Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems" by Hendrik Kleikamp, Martin Lazar, and Cesare Molinari.

You find the paper here (the preprint is available here).

Installation

On a system with git (sudo apt install git), python3 (sudo apt install python3-dev) and venv (sudo apt install python3-venv) installed, the following commands should be sufficient to install the ml-control package with all required dependencies in a new virtual environment:

git clone https://github.com/HenKlei/ML-OPT-CONTROL.git
cd ML-OPT-CONTROL
python3 -m venv venv
source venv/bin/activate
pip install -r requirements.txt
pip install .

Running the experiments

To reproduce the results, we provide the original scripts creating the results presented in the paper in the directory ml_control/examples/.

To apply the greedy algorithm and the machine learning reduced models for the heat equation example, run the script heat_equation_greedy_complex.py. If you would like to create plots of optimal final time adjoints, optimal controls and states, run the script heat_equation_plots_complex.py. We also provide different parametrizations and problem settings that are not contained in the paper in the folder heat_equation/.

To apply the greedy algorithm and the machine learning reduced models for the damped wave equation example, run the script damped_wave_equation_greedy.py. If you would like to create plots of optimal final time adjoints, optimal controls and states, run the script damped_wave_equation_plots.py. We also provide different parametrizations and problem settings that are not contained in the paper in the folder wave_equation/.

Questions

If you have any questions, feel free to contact us via email at hendrik.kleikamp@uni-graz.at.