Identification problems in stochastic control theory

2020 Fiscal Year Final Research Report

• Project/Area Number: 17K05359
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Nakano Yumiharu 東京工業大学, 情報理工学院, 准教授 (00452409)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 部分観測確率制御 / 逆問題

Outline of Final Research Achievements

For the inverse problem in stochastic optimal control theory, we have clarified the sufficient conditions for well-posedness in the proposed framework. The numerical solutions are also discussed, and it is confirmed numerically that the penalty parameters are reproduced with high accuracy for some specific problems.
For the numerical analysis of the partial observation stochastic control problem, based on the discussion of the convergence of the kernel-based method for the Zakai equation, which characterizes the partial observation problem for diffusion processes, the original problem is approximated by an finite-dimensional complete observation stochastic control problem and the error evaluation is given. This means that we give a method to approximate the infinite-dimensional Hamilton-Jacobi-Bellman equation corresponding to the partial observation stochastic control problem by that of finite dimension.

Free Research Field

確率制御理論

Academic Significance and Societal Importance of the Research Achievements

これまで，確率制御の一般的枠組みにおいて逆問題はほとんど研究されておらず，また，決定論的制御においても逆問題の適切性を議論した論文は無いため，本成果は，最適制御の逆問題という，長年重要視されてきた問題に対し理論的基盤の一つを与えるものと位置付けられる．さらに，部分観測確率制御問題に対して実装可能な数値解法を初めて提供した．
本研究の貢献は，非線形確率システム同定・制御の実用化に必要な部分の数値解析の端緒として位置付けられ，これを基に広範囲の応用分野の発展が期待できる．