A fundamental problem in science and engineering is designing optimal control policies that steer a given system towards a desired outcome. This work proposes Control Physics-Informed Neural Networks (Control PINNs) that simultaneously solve for a given system state, and for the optimal control signal, in a one-stage framework that conforms to the underlying physical laws. Prior approaches use a two-stage framework that first models and then controls a system in sequential order. In contrast, a Control PINN incorporates the required optimality conditions in its architecture and in its loss function. The success of Control PINNs is demonstrated by solving the following open-loop optimal control problems: (i) an analytical problem, (ii) a one-dimensional heat equation, and (iii) a two-dimensional predator-prey problem.
@article{arxiv.2205.03377,
title = {Physics-informed neural networks for PDE-constrained optimization and control},
author = {Jostein Barry-Straume and Arash Sarshar and Andrey A. Popov and Adrian Sandu},
journal= {arXiv preprint arXiv:2205.03377},
year = {2022}
}