1998 Fiscal Year Final Research Report Summary
Studies on Mathematical Structure of Dynamic Programming
| Project/Area Number |
09640243
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Chiba University |
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Principal Investigator |
KURANO Masami Chiba Univ., Faculty of Education, Prof., 教育学部, 教授 (70029487)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIDA Yuji Kitakyushu Univ., Faculty of Economics, Prof., 経済学部, 教授 (90192426)
KADOTA Yoshinobu Wakayama Univ., Faculty of Education, Prof., 教育学部, 教授 (90116294)
MARUYAMA Ken-ichi Chiba Univ., Faculty of Education, Asist.Prof., 教育学部, 助教授 (70173961)
KENMOCHI Nobuyuki Chiba Univ., Faculty of Education, Prof., 教育学部, 教授 (00033887)
UZAWA Masakazu Chiba Univ., Faculty of Education, Prof., 教育学部, 教授 (80009026)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Dynamic Programming / Markov Decision Processes / Fuzzy Dynamic System / Markov Set-Chain / Fuzzy Stopping / Optimality Equation / general Utility / Optimal Policy |
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| Research Abstract |
In this project, our objective is to develope the structural study of Dynamic Programming(DP in short) and establish DP method which is more robust or more flexible in the sense that it is reasonably efficient in rough approximation and allows for fluctuating factors in sequential decision processes.
For this purpose. we tried to develope analytical studies on various mathematical decion model.
(1) Markov set-chain model As a model which is robust for rough approximation of the transition matrix in Markov decision processes, we introduced a decision model, called a controlled Markov set-chain, and derived a DP equation by which Pareto optimal policies was constructed. Some computational results are included.
(2) Fuzzy dynamic systems and stopping problem The ergodic theorem for the dynamic system with fuzzy state and fuzzy transition is developed and the existence and uniqueness of solutions of the corresponding DP equations is proved. Also, a stopping problem for dynamic fuzzy system is formulated and solved by an extended UP method.
(3) General utility model A stopped Markov decision process is analysed under general utility. The corresponding DP equation is described by a family of distributions and more usefull in application of DP.
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