Optimal Control Duality and the Douglas-Rachford Algorithm
Optimization and Control
2023-10-24 v2
Abstract
We explore the relationship between the dual of a weighted minimum-energy control problem, a special case of linear-quadratic optimal control problems, and the Douglas-Rachford (DR) algorithm. We obtain an expression for the fixed point of the DR operator as applied to solving the optimal control problem, which in turn devises a certificate of optimality that can be employed for numerical verification. The fixed point and the optimality check are illustrated in an example optimal control problem.
Cite
@article{arxiv.2303.06527,
title = {Optimal Control Duality and the Douglas-Rachford Algorithm},
author = {Regina S. Burachik and Bethany I Caldwell and C. Yalçın Kaya and Walaa M. Moursi},
journal= {arXiv preprint arXiv:2303.06527},
year = {2023}
}