Robust stability analysis of infinite-dimensional sampled-data systems

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K14362
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Kobe University
• Principal Investigator: Wakaiki Masashi 神戸大学, システム情報学研究科, 准教授 (50778587)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 強連続半群 / サンプル値系 / 安定性解析 / 半一様安定性 / 多項式安定性

Outline of Final Research Achievements

We have dealt with infinite-dimensional systems described by delay differential equations or partial differential equations. We have derived conditions for preserving the stability of perturbed sampled-data control systems. Then, using the insights from this robust stability analysis, we have established a theory of event-triggered control and self-triggered control, in which the plant outputs are measured and the control inputs are updated only when necessary. Furthermore, we have focused on semi-uniform stability, which is a weaker stability concept than uniform exponential stability previously studied, and have estimated the decay rate of time-discretized semi-uniformly stable systems.

Free Research Field

無限次元系の解析・制御

Academic Significance and Societal Importance of the Research Achievements

近年の情報通信技術の発展に伴い，通信ネットワークとコンピュータを活用した制御が主流となっている．これは，偏微分方程式や遅延微分方程式で表現される無限次元系も例外ではない．本研究で構築した解析手法により，無限次元系に対するサンプル値制御の安全性を理論的に保証できるようになった．さらに，センサの消費電力やデータ通信頻度を考慮した設計理論を構築したことで，無限次元系の制御において安全性と省資源・省エネルギー化を同時に実現することが可能となった．