Reduced Model Reconstruction Method for Stable Positive Network Systems

• 成果类型: Article
• 署名作者: Sato, Kazuhiro
• 署名单位: University of Tokyo; University of Tokyo
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3218620
• 发表日期: 2023
• 页码: 5616-5623
• 关键词: Model reduction; network system; optimization; positive system

摘要

We consider a reconstruction problem of a reduced stable positive network system with the preservation of the original interconnection structure based on an H-2 optimal model reduction problem with constraints. To this end, we define an important set using the Perron-Frobenius theory of nonnegative matrices such that all elements of the set are stable and Metzler. Using the projection onto the set, we propose a cyclic projected gradient method to produce a better reduced model than an initial reduced model in the sense of the H-2 norm. In the method, we use Lipschitz constants of the gradients of our objective function to define the step sizes without a line search method whose computational complexity is large. Moreover, the existence of the Lipschitz constants guarantees the global convergence of our proposed algorithm to a stationary point. The numerical experiments demonstrate that the proposed algorithm improves a given reduced model, and can be used for large-scale systems.