Development of Advanced Stochastic Control Methods Utilizing Probability Distributions

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K13779
• 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: Kyoto University (2019-2022); Aoyama Gakuin University (2018)
• Principal Investigator: Hoshino Kenta 京都大学, 情報学研究科, 助教 (10737498)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 制御理論 / 確率制御 / 最適制御 / 安定性理論 / 最適輸送

Outline of Final Research Achievements

This project aimed to develop control methods for stochastic systems with a particular focus on probability distributions associated with stochastic control systems. Mainly, it focused on optimal control problems and stability analysis. Regarding the optimal control problems, this project has established optimality conditions for steering problems of probability distributions. The cost in the optimal control problems is designed using the Wasserstein distances based on the optimal transport theory. Furthermore, this project focused on the finite-time stability of stochastic systems. The analysis developed in this project enables the analysis of the distribution of a settling time of stability. Moreover, the analysis was applied to the safe control problem, a recent control engineering topic.

Free Research Field

制御理論

Academic Significance and Societal Importance of the Research Achievements

近年，制御工学で扱うシステムの大規模化および多様化により，確定的な枠組みでは取り扱いの難しいシステムの制御へのニーズが高まっている．また，深層学習における生成モデルの一部は確率動的システムとして扱いうることが知られている．本課題はそのような動向に着目し，確率制御システムの制御問題について，不確実性やデータとの親和性を考慮した際に重要となる確率分布の概念に重点をおいた制御手法の開発に取り組んだ．その結果，生成モデルへと応用可能な最適性条件の導出や確率的な不確実性を伴うシステムの安全制御の手法の開発などが達成され，制御工学や関連分野への波及効果が期待できる成果が得られた．