Introduction

This repo contains the code for the two papers

• Counter-example guided synthesis of neural network Lyapunov functions for piecewise linear systems
  Hongkai Dai, Benoit Landry, Marco Pavone and Russ Tedrake
  IEEE Conference on Decision and Control, 2020
  video
• Lyapunov-stable neural-network control
  Hongkai Dai, Benoit Landry, Lujie Yang, Marco Pavone and Russ Tedrake
  Robotics: Science and Systems, 2021
  video

We can synthesize neural-network controllers with Lyapunov stability guarantees. Namely for all the initial states within a certain region, the controller will drive the system from these initial states to converge to the goal state.

Setup

Python requirements

We use python 3 in this project. You could first install the packages in requirements.txt.

Install gurobi

Please download gurobi from https://www.gurobi.com/products/gurobi-optimizer/. We require at least gurobi 9.5. After downloading the software, please install its Python API by following https://www.gurobi.com/documentation/9.0/quickstart_mac/the_grb_python_interface_f.html

To check your gurobi installation, type the following command in your terminal:

$ python3 -c "import gurobipy"

There should be no error thrown when executing the command.

Setup environment variable

In the terminal, please run

$ python3 setup.py

It will print out the command to setup the environment variables. Execute that command in your terminal.

Run a toy example

You could run

$ python3 neural_network_lyapunov/test/train_toy_system_controller_demo.py --dimension=1

This will synthesize a stabilizing controller with a Lyapunov function for a toy 1D system (TODO: add some visualization at the end of the demo). You should see that the error printed on the screen decreases to almost 0. (The code is non-deterministic, so if it doesn't converge to 0 in the first trial, you can re-run the demo and hopefully it converges in the second trial).

Contributing to repo

Linting

We use flake8 to check if the python code follows PEP standard. Before submitting the PR, you could run

$ cd neural_network_lyapunov
$ flake8 ./

to check if there are any violations.

Unit test

I am a strong believer of unit test. We strongly encourage to add tests to the functions in the PR.