An approach to the control theory by analytic and geometric methods.

通过解析和几何方法研究控制理论。

• 批准号: 02640192
• 负责人: ISHIGAKI Haruo
• 金额: $ 0.51万
• 依托单位: Waseda Univ.
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1990
• 资助国家: 日本
• 起止时间: 1990 至 1991
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02640192/
• 关键词: Control Theory; Random Process; Portofolio; Stochastic differential Equation; Semigroup Theory; cox'sモデル; ランダム・プロセス; 最適問題; HーJーB方程式; ポ-トフォリオ; Kulbackの情報量; 確率過程; 最適制御; 発展作用素; 力学系; Dynamic programing

There are many control problems of the systems described as a random process. For example, H-J-B equation was derived from optimal control problems subject to the stochastic differential equation. These equations have viscosity solutions but non usual solution.We have tried to obtain a semigroup solution and to characterize the optimal control. For very special case, a kind of portfolio problem, we could express the solution in direct form, and get a criterion of optimality.The other hand, We have tried to extend the semigroup theory, and obtained some results about the C-semigroup.Another our results are about the space of continuous functions as the space of sample pathes. As a gcometric approach, We have studied the graph theory.

被描述为随机过程的系统有许多控制问题。例如，H-J-B方程来自受随机微分方程的最佳控制问题。这些方程式具有粘度解决方案，但非通常的解决方案。我们试图获得半群解决方案并表征最佳控制。对于非常特殊的情况，一种投资组合问题，我们可以直接表达解决方案，并获得最优性标准。另一方面，我们试图扩展半群理论，并获得了有关c-序列的一些结果。另一方面，我们的另一个结果涉及连续功能作为样品路径空间的连续功能。作为GCometric方法，我们研究了图理论。

项目成果

Hiroyuki Takagi and Junzo Wada: "Weakly Compact Weighted Composition Operators on Certain Subspaces of C(X, E)" Proceedings of the Japan Academy. Vol. 67, Ser. A, No. 9. 304-307 (1991)

Hiroyuki Takagi 和 Junzo Wada：“C(X, E) 某些子空间上的弱紧紧加权组合算子”日本学院院刊。

垣田 高夫: "On WhitneyーSchmarty Thesem" RIMS. 28. (1992)

Takao Kakita：“论惠特尼-施马蒂这些”RIMS 28。（1992）

和田 淳蔵: "Weakly compact weeghted composition okeratoro on centain anhsraceoof C(XE)" Prog.Japan Acad.67. 304-307 (1991)

Junzo Wada：“C(XE) 上的弱紧凑加权组合 okeratoro”Prog.Japan Acad.67 (1991)。

鈴木 晋一: "Some Pemargam Knots and links in sqecial grajhs" Proc.Knoto '90,Nalter ae Grnyter. (1992)

Shinichi Suzuki：“seqecial grajhs 中的一些 Pemargam 结和链接”Proc.Knoto 90，Nalter ae Grnyter (1992)。

和田 淳蔵: "Weakly compact Weighted composition operators on certain subspoces of C(X,E)" Proceeding of the Japan Academy. Vol.67serA No9. (1991)

Junzo Wada：“C(X,E) 某些子点上的弱紧凑加权合成算子”日本科学院院刊第 67 卷 A 第 9 期（1991 年）。