BCHOL-python

Python proof of concept for BCHOL: A Parallel linear system solver for optimal control.

Table of Contents

1. Introduction
2. Requirements
3. Installation
4. Usage
5. Citing

Introduction

Solves for x in Ax = b, using the Recursive Schur Linear Quadratic Regulator explained in the paper A Parallell Linear System Solver for Optimal Control by Brian E.Jackson. It requires A to be a positive semi-definite matrix to guarantee a good result.

This method is part of the Python implementation of trajectory optimization (trajopt) algorithms and model predictive control (MPC). Learn more about different TrajoptMPC here.

Requirements

• Python 3.10+
• Libraries:
  • Numpy
  • SciPy

Instalation

• The following libraries (Numpy, Scipy) are included in the requirments.txt and can be downloaded with the following command

git clone https://github.com/A2R-Lab/BCHOL-python.git
pip3 install -r requirements.txt

Usage

If you already have a defined LQR problem in a KKT form in a saved file .json/.csv you can look at solve_load.py for an example of how to load the problem. The program will return the solution in two forms:

1. Flattened dxul vector
2. Brian Jackson's format as mentioned in the paper [lambda_i ; x_i; u_i]

python solve_load.py

If you just have an A matrix and a b vector look at solve_build.py for an example of usage. Alternatively, you can use this package as part of our bigger solverhere.

Citing

Author: Yana Botvinnik Contact: ybotvinn@barnard.edu