Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.09753 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912521745596416 |
|---|---|
| author | Yang, Zhaohua Yang, Nachuan Wang, Pengyu Zhang, Haishan Xu, Xiayan Shi, Ling |
| author_facet | Yang, Zhaohua Yang, Nachuan Wang, Pengyu Zhang, Haishan Xu, Xiayan Shi, Ling |
| contents | This paper addresses the problem of the optimal $H_2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interior-Point-based H2 Controller Synthesis for Compartmental Systems Yang, Zhaohua Yang, Nachuan Wang, Pengyu Zhang, Haishan Xu, Xiayan Shi, Ling Optimization and Control This paper addresses the problem of the optimal $H_2$ 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. |
| title | Interior-Point-based H2 Controller Synthesis for Compartmental Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2406.09753 |