Interior-Point-based H2 Controller Synthesis for Compartmental Systems
Abstract
This paper addresses the problem of the optimal controller design for compartmental systems. In other words, we aim to enhance system robustness while maintaining the law of mass conservation. We perform a novel problem transformation and establish that the original problem is equivalent to an new optimization problem with a closed polyhedron constraint. Existing works have developed various first-order methods to tackle inequality constraints. However, the performance of the first-order method is limited in terms of convergence speed and precision, restricting its potential in practical applications. Therefore, developing a novel algorithm with fast speed and high precision is critical. In this paper, we reformulate the problem using log-barrier functions and introduce two separate approaches to address the problem: the first-order interior point method (FIPM) and the second-order interior point method (SIPM). We show they converge to a stationary point of the new problem. In addition, we propose an initialization method to guarantee the interior property of initial values. Finally, we compare FIPM and SIPM through a room temperature control example and show their pros and cons.
Cite
@article{arxiv.2406.09753,
title = {Interior-Point-based H2 Controller Synthesis for Compartmental Systems},
author = {Zhaohua Yang and Nachuan Yang and Pengyu Wang and Haishan Zhang and Xiayan Xu and Ling Shi},
journal= {arXiv preprint arXiv:2406.09753},
year = {2025}
}