1. Interior-Point-based H2 Controller Synthesis for Compartmental Systems
- Author
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Yang, Zhaohua, Yang, Nachuan, Wang, Pengyu, Zhang, Haishan, Xu, Xiayan, and Shi, Ling
- Subjects
Mathematics - Optimization and Control - Abstract
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.
- Published
- 2024