DeePC

Description

This repository provides a Python package and a C++ library, which both implement DeePC from the paper
Data-Enabled Predictive Control: In the Shallows of the DeePC
https://arxiv.org/pdf/1811.05890

Requirements

Python

The Python package requires at least Python 3.10 and pip.
It depends on numpy, which it installs automatically through pip.

C++

The C++ library requires a C++ compiler, cmake, and make.
It depends on Eigen, Google Test, and Google Benchmark; which it installs automatically through cmake.

Installation

Python

To install the Python package deepc, run pip install ..
It installs the package and all its dependencies.
(Use pip install -e . to install it in editable mode.)
To run the provided tests, execute python -m unittest discover tests/deepc.
(The GitHub actions run them on every commit.)

C++

To build the C++ library into a folder build, run

cmake -B build
make -C build

To run the provided tests, execute make -C build test.
(The GitHub actions run them on every commit.)
To install the library, execute make -C build install.
To list more options of make, see make --help.

Usage

The DeePC algorithm calculates the optimal control for a given system and a target.
To grasp the system it requires data from an offline procedure in the form of system input data u_d and system output data y_d. To grasp the current stat of the system it needs initialization data in the form of system input data u_ini and system output data y_ini.
With this data it solves

\begin{aligned}
    &\text{minimize}_{g, u, y} \quad \| y - r \|_Q^2 + \| u - u_0 \|_R^2 \\
    &\text{subject to} \quad \begin{pmatrix} U_p \\ Y_p \\ U_f \\ Y_f \end{pmatrix} g = \begin{pmatrix} u_{\text{ini}} \\ y_{\text{ini}} \\ u \\ y \end{pmatrix} \\
    &\quad u \in \mathcal{U}
\end{aligned}

where

\| x \|_A := x^T A x

\begin{pmatrix} U_p \\ U_f \end{pmatrix} := \mathcal{H}_{T_{\text{ini}}+N}(u_d), \begin{pmatrix} Y_p \\ Y_f \end{pmatrix} := \mathcal{H}_{T_{\text{ini}}+N}(y_d)

and H denotes the hankel matrix.
Note that this is more general than described in the paper.
The resulting u is the optimal control to reach the target r in the context of the optimization problem.

Python

The Python package provides two implementations of this, the stand-alone algorithm deePC and a controller.
For reference applications of the controller see example_1d.ipynb and example_3d.ipynb.

C++

The C++ library provides two implementations of this, the stand-alone algorithm deePC and a controller.