BCHOL-python

Python proof of concept for BCHOL.

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+

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

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. 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.

Both files will return an xyz solution vector in dxul.

Citing

Author: Yana Botvinnik Contact: ybotvinn@barnard.edu