Optimal node scheduling of network systems using dynamic sparse modeling

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K14188
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 21040:Control and system engineering-related
• Research Institution: The University of Kitakyushu
• Principal Investigator: Ikeda Takuya 北九州市立大学, 国際環境工学部, 准教授 (00848319)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: スパース制御 / 最適制御 / ネットワークシステム / ノード選択 / 可制御性 / 凸最適化 / マルチエージェントシステム

Outline of Final Research Achievements

We have studied an optimization problem of maximizing controllability Gramians under sparsity constraints, elucidating the mathematical characteristics of the optimal solution and proposing effective numerical algorithms. First, we have shown that this problem can be equivalently expressed as a certain optimal control problem from the controllability Lyapunov differential equation. By applying the maximum principle to this optimal control problem, we have derived a set of necessary conditions for an optimal solution. Based on this property, we have derived a sufficient condition under which this problem is equivalent to a convex optimization problem. Second, we have characterized the parallelepiped that is tangent to the reachable set, from which we have derived a linear approximation of the cost function. Although the approximate solution using this method is inferior to the solution of the convex relaxation method, it has the advantage of being computationally less demanding.

Free Research Field

制御理論

Academic Significance and Societal Importance of the Research Achievements

本研究で考察する動的スパースモデリングは理論的に新しいだけでなく，省エネルギーと通信制約を同時に最適化に取り入れた制御理論として学術的意義がある．また，本研究の応用範囲には無人航空機により構成されるマルチエージェントシステムの制御が含まれ，農業における農薬散布や航空写真の撮影等の産業的な応用のほか，巨大地震や広域火災などによる災害調査や探索などの急務かつ重要な応用がある．そのほか，ネットワークを内部に有する大規模系の設計理論は，制御理論分野のみならず情報工学や脳神経科学等の多岐にわたる分野に応用があり，その理論の確立により先端技術の発展が期待できる．