Closed-Loop Koopman Operator Approximation

This repository contains the companion code for Closed-Loop Koopman Operator Approximation. All the code required to generate the paper's plots from raw data is included here.

The regression methods detailed in the paper are implemented in cl_koopman_pipeline.py, which extends pykoop, the authors' Koopman operator identification library.

This software relies on doit to automate experiment execution and plot generation.

Requirements

This software is compatible with Linux, macOS, and Windows. It was developed on Arch Linux with Python 3.11.6, while the experiments used in the corresponding paper were run on Windows 10 with Python 3.10.9. The pykoop library supports any version of Python above 3.7.12. You can install Python from your package manager or from the official website.

Installation

To clone the repository, run

$ git clone [email protected]:decargroup/closed_loop_koopman.git

The recommended way to use Python is through a virtual environment. Create a virtual environment (in this example, named venv) using

$ virtualenv venv

Activate the virtual environment with¹

$ source ./venv/bin/activate

To use a specific version of Python in the virtual environment, instead use

$ source ./venv/bin/activate --python <PATH_TO_PYTHON_BINARY>

If the virtual environment is active, its name will appear at the beginning of your terminal prompt in parentheses:

(venv) $

To install the required dependencies in the virtual environment, including pykoop, run

(venv) $ pip install -r ./requirements.txt

The LMI solver used, MOSEK, requires a license to use. You can request personal academic license here. You will be emailed a license file which must be placed in ~/mosek/mosek.lic².

Usage

To automatically generate all the plots used in the paper, run

(venv) $ doit

in the repository root. This command will preprocess the raw data located in dataset/, run all the required experiments, and generate figures, placing all the results in a directory called build/.

To execute just one task and its dependencies, run

(venv) $ doit <TASK_NAME>

To see a list of all available task names, run

(venv) $ doit list --all

For example, to generate only the closed-loop prediction error plot, run

(venv) $ doit plot_paper_figures:errors_cl

If you have a pre-built copy of build/ or other build products, doit will think they are out-of-date and try to rebuild them. To prevent this, run

(venv) $ doit reset-dep

after placing the folders in the right locations. This will force doit to recognize the build products as up-to-date and prevent it from trying to re-generate them. This is useful when moving the build/ directory between machines.

Dataset

The dataset contained in dataset/ was collected using the Quanser QUBE-Servo. Details concerning the experimental procedure can be found in the paper. The C source code used to run the QUBE-Servo system can be found here.

Each CSV file in dataset/ contains one experimental episode. The columns are:

Column	Description
t	Timestamp (s)
target_theta	Target motor angle (rad)
target_alpha	Target pendulum angle (rad)
theta	Measured motor angle (rad)
alpha	Measured pendulum angle (rad)
control_output	Control signal calculated by the controller (V)
feedforward	Feedforward signal to be added to control_output (V)
plant_input	control_output summed with feedforward (V), saturated between -10V and 10V
saturation	Signal indicating if saturation is active (i.e., -1 if saturating in the negative direction, +1 if saturating in the positive direction)

Repository Layout

The files and folders of the repository are described here:

Path	Description
build/	Contains all doit outputs, including plots.
dataset/	Contains the raw experimental data from the Quanser QUBE-Servo system.
cl_koopman_pipeline.py	Contains implementations of algorithms presented in the paper.
dodo.py	Describes all of doit's behaviour, like a Makefile. Also contains plotting code.
LICENSE	Repository license.
requirements.txt	Contains required Python packages with versions.
README.md	This file!

Footnotes

1. On Windows, use > \venv\Scripts\activate. ↩

2. On Windows, place the license in C:\Users\<USER>\mosek\mosek.lic. ↩