Construction of Control Theory for Positive Systems Using Conic Programming

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K04200
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 21040:Control and system engineering-related
• Research Institution: Kyushu University (2019-2021); Kyoto University (2018)
• Principal Investigator: Ebihara Yoshio 九州大学, システム情報科学研究院, 教授 (80346080)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: 錐計画 / 非負システム / 制御系の解析と設計

Outline of Final Research Achievements

In this study we develop conic-programming-based analysis and synthesis of　linear positive dynamical systems. In dealing with the analysis and synthesis of　general (non-positive) linear dynamical systems, the effectiveness of the　semidefinite programming problem (SDP) is widely recognized where an SDP is an　optimization problem over the positive semidefinite cone. However, when dealing　with the analysis and synthesis of positive systems with strong positive　properties, it is natural to employ the copositive programming problem (COP)　where a COP is an optimization problem over the copositive cone. From this view　point, we mainly derived COP-based analysis and synthesis conditions for positive　systems in this study.

Free Research Field

制御理論

Academic Significance and Societal Importance of the Research Achievements

非負システムとは，非負の入力と非負の初期状態に対して，状態と出力が常に非負になるという性質を有する動的システムである．このような入力・状態・出力の非負性は，資源，エネルギー，製品，化学物質といった“負の値を取り得ない物理量”のやりとりを表すダイナミクスにおいて普遍的に現れる．本研究ではとくに，非負値信号の取り扱いにおいて有効であるものの，制御理論分野ではあまりその有用性が知られていない共正値計画という特殊な最適化問題を利用し，非負システムの解析と設計に関して理論的な成果を獲得した．