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2023 Fiscal Year Final Research Report

Studies of dynamic programming partial differential equations related to optimal control in path-dependent systems

Research Project

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Project/Area Number 20K03733
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionKumamoto University (2021-2023)
Osaka University (2020)

Principal Investigator

Kaise Hidehiro  熊本大学, 大学院先端科学研究部(理), 教授 (60377778)

Project Period (FY) 2020-04-01 – 2024-03-31
Keywords最適制御 / 動的計画法 / 動的計画偏微分方程式 / 粘性解
Outline of Final Research Achievements

Optimal control is the theory to control time-varying states of systems under given criteria. In usual optimal control, it is assumed that systems have Markov property which means the future state of the system is determined by the current state. On the other hand, path-dependent systems where future states also depend on past states attract interests of researchers in various fields including engineering. In this research project, we obtained results on dynamic programming methods for path-dependent systems, also for systems which are not included in conventional frames of systems.

Free Research Field

最適制御

Academic Significance and Societal Importance of the Research Achievements

動的計画法は、主体者が系の状態をコントロールするための強力な手法である。マルコフ性を持つ系に対する動的計画法に関しては膨大な研究成果があり、様々な分野の問題を動機として今もなお多くの研究者により研究がなされているが、経路依存系に対する動的計画法の一般論の研究は少ない。本研究課題では、経路依存性を持つ系に関連する動的計画偏微分方程式の研究を行い、経路依存系における基準の最適値を求めるための基礎理論を築いた。また、複素空間を状態空間に持つ系に対する動的計画法を進展させた。

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Published: 2025-01-30  

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