跳到主要內容

臺灣博碩士論文加值系統

(3.233.217.106) 您好!臺灣時間:2022/08/17 22:23
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:李淵順
研究生(外文):Yuan-Shun Lee
論文名稱:一些微分對局問題之論點
論文名稱(外文):Some Aspects of Differential Game Problems
指導教授:謝哲光謝哲光引用關係
指導教授(外文):Jer-Guang Hsieh
學位類別:博士
校院名稱:國立中山大學
系所名稱:電機工程學系研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:131
中文關鍵詞:多對一追逐逃逸微分對局微分對局二對二城堡攻防微分對局效能指標可切換微分對局最佳策略推理策略
外文關鍵詞:pursuit-evasion game with n pursuers and one evaoptimal strategyguarding a territory with two guarders and two idifferential gamereasoning strategypayoff-switching differential game
相關次數:
  • 被引用被引用:0
  • 點閱點閱:266
  • 評分評分:
  • 下載下載:13
  • 收藏至我的研究室書目清單書目收藏:0
摘 要
在我們日常生活中所遭遇到的實際對局問題通常是複雜的,因此現有處理對局的方法不足以被用來解決它們。這促使我們在本論文中研究幾個還未被考慮過或尚未被完全解決的微分對局問題,包括n個追逐者與一個逃逸者的追逐逃逸對局、二個防衛者與二個入侵者的城堡攻防對局及指標函數可切換微分對局問題。
在本論文中,我們首先利用幾何的方法來考慮n個追逐者與一個逃逸者的追逐逃逸對局。兩個可以用來決定在某些情況下此對局解值的法則將被提出,在此我們可以發現一個追逐者與一個逃逸者的追逐逃逸對局是此問題的一個特例。
接著我們將對二個防衛者與二個入侵者的城堡攻防對局作定性與定量的分析。透過本問題之研究,一些從未在一個防衛者與一個入侵者的城堡攻防對局中出現的情況將被顯露出來。一個在本研究中有趣的發現是,在某些情況下為了得到一個較佳的結果,入侵者或許需要扮演追逐者的角色,這將使得本問題更複雜也更難解決。
最後我們首度提出一個具有不完全對局資訊的指標函數可切換微分對局問題。此問題與傳統微分對局的最主要差異在於參與者在對局進行當中可以任意切換指標函數,這使得此類問題的最佳性無法得到保證。一些根據不同方法的推理機制將被提出,用來決定某一個參與者的推理策略。我們將以一個實際的三城堡攻防對局問題來說明指標函數可切換微分對局的情況。多個電腦模擬將被用來比較不同推理策略的性能。指標函數可切換微分對局理論的提出對於處理具有不完全對局資訊的微分對局問題是一個重大的突破。
ABSTRACT
Usually, real game problems encountered in our daily lives are so complicated that the existing methods are no longer sufficient to deal with them. This motivates us to investigate several kinds of differential game problems, which have not been considered or solved yet, including a pursuit-evasion game with n pursuers and one evader, a problem of guarding a territory with two guarders and two invaders, and a payoff-switching differential game.
In this thesis, firstly the geometric method is used to consider the pursuit-evasion game with n pursuers and one evader. Two criteria used to find the solutions of the game in some cases are given. It will be shown that the one-on-one pursuit-evasion game is a special case of this game.
Secondly, the problem of guarding a territory with two guarders and two invaders is considered both qualitatively and quantitatively. The investigation of this problem reveals a variety of situations never occurring in the case with one guarder and one invader. An interesting thing found in this investigation is that some invader may play the role as a pursuer for achieving a more favorable payoff in some cases. This will make the problem more complicated and more difficult to be solved.
The payoff-switching differential game, first proposed by us, is a kind of differential game with incomplete information. The main difference between this problem and traditional differential games is that in a payoff-switching differential game, any one player at any time may have several choices of payoffs for the future. The optimality in such a problem becomes questionable. Some reasoning mechanisms based on different methods will be provided to determine a reasoning strategy for some player in a payoff-switching differential game. A practical payoff-switching differential game problem, i.e., the guarding three territories with one guarder against one invader, is presented to illustrate the situations of such a game problem. Many computer simulations of this example are given to show the performances of different reasoning strategies. The proposition of the payoff-switching differential game is an important breakthrough in dealing with some kinds of differential games with incomplete information.
CONTENTS
誌謝 ……………………………………………………………………………iii
摘要 ……………………………………………………………………………iv
ABSTRACT ………………………………………………………………………………… v
GLOSSARY OF SYMBOLS ………………………………………………………… vii
CHAPTER IINTRODUCTION ………………………………………………………… 1
Section 1.1Motivation ……………………………………………1
Section 1.2Brief Sketch of the Contents……………………4
CHAPTER IIDIFFERENTIAL GAMES …………………………………5
Section 2.1General Concept …………………………………5
Section 2.2Two-person Zero-sum Differential Games ………8
Section 2.2.1Pursuit-evasion Game with One Pursuer and One
Evader ………………………………………………10
Section 2.2.2Guarding a Territory with One Guarder and One
Invader ………………………………………………16
CHAPTER IIIMULTI-PERSON DIFFERENTIAL GAMES ……………22
Section 3.1Pursuit-evasion Game with n Pursuers and One
Evader ……………………………………………… 23
Section 3.2Guarding a Territory with Two Guarders and
Two Invaders………………………………………… 42
Section 3.2.1Preliminaries …………………………………42
Section 3.2.2Problem Formulation and Definitions …………44
Section 3.2.3Qualitative Analysis ………………………………48
Section 3.2.4Quantitative Analysis ………………………56
CHAPTER IVPAYOFF-SWITCHING DIFFERENTIAL GAMES …………………… 77
Section 4.1Differential Games with Incomplete
Information …………………………………………77
Section 4.2Payoff-switching Differential Games …………81
Section 4.3Reasoning Mechanisms for a Payoff-switching
Differential Game ………………………………… 87
Section 4.3.1A Traditional Reasoning Mechanism by Computing
Minimum Payoff………………………………………… 88
Section 4.3.2A General Reasoning Algorithm for a Payoff-
switching Differential Game ……………………… 90
Section 4.3.3A Strategy for a Payoff-Switching Differential
Game Based on Fuzzy Reasoning…………………… 97
Section 4.3.4Using Similarity Measure to Estimate the
Player’s Behavior in a Payoff-switching
Differential Game…………………………………… 108
CHAPTER VCONCLUSIONS AND DISSCUSSIONS …………………116
REFERENCES…………………………………………………………119
REFERENCES
[Ard.1]M. Ardema, M. Heymann and N. Rajan, Combat games, Journal of Optimization Theory and Applications, Vol. 46, pp. 391-398, 1985.
[Baş.1]T. Başar and G.J. Olsder, Dynamic Noncooperative Game Theory, Academic Press, London, New York, 1982.
[Baş.2]T. Başar and G.J. Olsder, Differential Games and Applications, Springer-Verlag, New York, 1988.
[Baş.3]T. Başar, A dynamic games approach to controller design: disturbance rejection in discrete-time, IEEE Transactions on Automatic Control, Vol. 36, pp. 936-952, 1991.
[Bel.1]R. Bellman, Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1957.
[Ber.1]L.D. Berkovitz, A variational approach to differential games, in: M. Dresher, L. S. Shapley and A.W. Tucker, Eds., Advances in Game Theory, Princeton University Press, Princeton, New Jersey, pp. 127-174, 1964.
[Bor.1]P. and W. Rzymowski, Avoidance of many pursuers in the simple motion case, Journal of Mathematical Analysis and Applications, Vol. 111, pp. 535-546, 1985.
[Bor.2]P. and W. Rzymowski, Evasion from many pursuers in the simple motion case, Journal of Mathematical Analysis and Applications, Vol. 135, pp. 75-80, 1988.
[Box.1]G.E.P. Box and G.M. Jenkins, Time Series Analysis, Forecasting and Control, Holden-Day, San Francisco, California, 1976.
[Bre.1]J.V. Breakwell, Football as a differential game, Journal of Guidance, Control, and Dynamics, Vol. 15, No. 5, pp. 1292-1294, 1992.
[Bre.2]J.V. Breakwell, Pursuit of a faster evader, Proceedings of NATO Advanced Study Institute, edited by J.D. Grote, D. Riedel Publishing Company, Dordrecht, Holland, pp. 243-256, 1974.
[Bre.3]J.V. Breakwell and P. Hagedorn, Point capture of two evaders in succession, Journal of Optimization Theory and Applications, Vol. 27, No. 1, pp. 89-97, 1979.
[Cas.1]J.H. Case, Applications of the theory of differential games to economic problems, in: H.W. Kuhn and G.P. Szego, Eds., Differential Games and Related Topics, North-Holland, Amsterdam, Holland, pp. 345-371, 1971.
[Chu.1]H.J. Chu, J.G. Hsieh, K.H. Hsia and L.W. Chen, Fuzzy differential game of guarding a movable territory, Information Sciences, Vol. 91, pp. 113-131, 1996.
[Chu.2]H.J. Chu, J.G. Hsieh, Y.S. Lee and K.H. Hsia, A pursuit-evasion game with one curvature constraint, Optimal Control Applications & Methods, Vol. 21, pp. 47-61, 2000.
[Dub.1]D. Dubois and H. Prade, Fuzzy sets in approximate reasoning─Part 1 & 2: Inference with possibility distributions, Fuzzy Sets and Systems, Vol. 40, pp. 143-244, 1990.
[Fol.1]M.H. Foley and W.E. Schmitendorf, A class of differential game with two pursuers versus one evader, IEEE Transactions on Automatic Control, Vol. 19, pp. 239-243, 1974.
[Fri.1]A. Friedman, Differential Games, American Mathematical Society, Rhode Island, 1974.
[Gai.1]B.R. Gaines, Foundations of fuzzy reasoning, International Journal of Man-Machine Studies, Vol. 8, pp. 623-668, 1976.
[Gup.1]N.K. Gupta, An overview of differential games, in: C.T. Leondes, ed., Control and Dynamic Systems: Advances in Theory and Applications, Vol. 17, Academic Press, New York, 1981.
[Hag.1]P. Hagedorn and J.V. Breakwell, A differential game with two pursuers and one evader, Journal of Optimization Theory and Applications, Vol. 18, No. 1, pp. 15-29, 1976.
[Háj.1]O. Hájek, Pursuit Games, Academic Press, New York, 1975.
[Hsi.1]K.H. Hsia and J.G. Hsieh, A first approach to fuzzy differential game problem: guarding a territory, Fuzzy Sets and Systems, Vol. 55, pp. 157-167, 1993.
[Hsi.2]K.H. Hsia, J.G. Hsieh and H.J. Chu, Fuzzy differential game of guarding a territory in the presence of an obstacle, Proceeding of the First European Congress on Fuzzy and Intelligent Technologies, Aachen, Germany, pp. 1250-1254, 1993.
[Hsi.3]K.H. Hsia, Research on the Fuzzy Differential Game Problems, Ph.D. Dissertation, National Sun Yat-Sen University, Kaohsiung, Taiwan, 1994.
[Hsi.4]K.H. Hsia and J.H. Wu, A Study on the data preprocessing in grey relation analysis, Journal of the Chinese Grey System Association, Vol. 1, No. 1, pp. 47-53, 1998. (in Chinese)
[Hsi.5]K.H. Hsia, Y.S. Lee and J.G. Hsieh, Differential game with approximate reasoning: reasoning differential game, International Journal of Approximate Reasoning, submitted, 1998.
[Isa.1]R. Isaacs, Differential Games, John Wiley & Sons, New York, 1965.
[Ke.1]J.S. Ke and G.T. Her, A fuzzy information retrieval system model, Proceeding of 1983 National Computer Symposium, Taiwan, pp. 147-155, 1983.
[Kra.1]N.N. Krasovskii and U.S. Osipov, On the theory of differential games with incomplete information, Soviet Math. Dokl., Vol. 15, No. 2, pp. 587-591, 1974.
[Lee.1]C.C. Lee, Fuzzy logic in control systems: fuzzy logic controller--part I & II, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 20, pp. 404-435, 1990.
[Lee.2]Y.S. Lee, K.H. Hsia and J.G. Hsieh, Pursuit-evasion game with two pursuers and one evader, 陸軍官校75週年校慶綜合學術研討會, 高雄, 台灣, pp. 100-109, 1999.
[Lee.3]Y.S. Lee, K.H. Hsia and J.G. Hsieh, A general solution of a pursuit-evasion game with n pursuers and one evader, Proceedings of 1999 IEEE Hong Kong Symposium on Robotics and Control, Hong Kong, Vol. 2, pp. 701-706, 1999.
[Lee.4]Y.S. Lee, K.H. Hsia and J.G. Hsieh, A fuzzy reasoning differential game, Proceedings of the Eighth International Fuzzy Systems Association World Congress, Taipei, Taiwan, Vol. 2, pp. 772-776, 1999.
[Lee.5]Y.S. Lee, K.H. Hsia and J.G. Hsieh, A problem of guarding a territory with two invaders and two defenders, Proceedings of 1999 IEEE International Conference on Systems, Man, and Cybernetics, Tokyo, Japan, 1999. Vol. 3, pp. 863-868, 1999.
[Lee.6]Y.S. Lee, K.H. Hsia and J.G. Hsieh, Guarding a territory with two defenders against two invaders: qualitative and quantitative analysis, Journal of Optimization Theory and Applications, submitted, 1999.
[Lee.7]Y.S. Lee, K.H. Hsia and J.G. Hsieh, A reasoning differential game based on similarity measure, Proceedings of the Sixth International Conference on Automation Technology, Taipei, Taiwan, Vol. 2, pp. 603-608, 2000.
[Lee.8]Y.S. Lee, K.H. Hsia and J.G. Hsieh, A strategy for a payoff-switching differential game based on fuzzy reasoning, Fuzzy Sets and Systems, accepted, 2001.
[Mam.1]E.H. Mamdani, Application of fuzzy logic to approximate reasoning using linguistic semantics, IEEE Transactions on Computers, C-26, pp. 1182-1191, 1977.
[Mer.1]A.W. Merz, Stochastic guidance laws in satellite pursuit-evasion, Computers and Mathematics with Applications, Vol. 13, pp. 151-156, 1987.
[Pet.1]L.A. Petrosjan, Differential Games of Pursuit, World Scientific, New Jersey, 1993.
[Qia.1]X. Qian, Differential games with information lags, SIAM Journal on Control and Optimization, Vol. 32, No. 3, pp. 808-830, 1994.
[Zad.1]L.A. Zadeh, Fuzzy sets, Information and Control, Vol. 8, pp. 338-353, 1965.
[Zad.2]L.A. Zadeh, Similarity relation and fuzzy orderings, Information Sciences, Vol. 3, pp. 177-206, 1971.
[Zad.3]L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning I, II, III, Information Sciences, Vol. 8, pp. 199-251; Vol. 9, pp. 43-80, 1975.
[Zad.4]L.A. Zadeh, A theory of approximate reasoning, in: J.E. Hayes, D. Mitchie, L.I. Mikulich, Eds., Machine Intelligence, Vol. 9, Wiley, New York, pp. 149-194, 1979.
[Zim.1]H.-J. Zimmermann, Fuzzy Set Theory-and Its Applications, 2nd ed., Kluwer Academic Press, Dordrecht-Boston, 1987.
[Zim.2]H.-J. Zimmermann, Fuzzy Sets, Decision Making, and Expert Systems, Kluwer Academic Publishers, Boston, 1993.
[Zwi.1]R. Zwick, E. Carlstein and D.R. Budescu, Measures of similarity among fuzzy concepts: a comparative analysis, International Journal of Approximate Reasoning, Vol. 1, pp. 221-242, 1987.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
無相關論文
 
1. 林慶陽、王進琦。1998。虱目魚背部肉與腹部肉之煉製品加工特性比較。食品科學 25:591-600。
2. 邱思魁、游昭玲、蕭泉源。1995。養殖虱目魚普通肉含氮萃取物成分之季節變化。食品科學 22:387-394。
3. 吳景陽。1981。小麥麵粉組成之麵包製作及生化性質。食品工業 13:17-21。
4. 吳景陽。1998。麵筋。食品工業月刊 30(7):46-54。
5. 郭煌林。1994。蛋白質與多醣類知交互作用在食品系統上之應用。食品工業 26:45-54。
6. 徐善宜。2001,2000年台灣農食品產業進出口分析。食品資訊。 184:28-33。
7. 孫寶年。1993。水產加工品之開發方向與理念。食品工業月刊 25(3):10-13。
8. 廖宏儒。2000。麵包中麵糰的物化特性。烘焙工業 89 : 68-73。
9. 陳勉之。1975。小麥蛋白質之組成即發酵麵食的製作功能。食品工業 7:15-18。
10. 陳輝煌、陳翠瑤、駱錫能。1996。鼬鮫魚漿在靜置期間化學鍵結及熱穩定性之變化。食品科學 23:66-76。
11. 陳美伶、柯文慶、賴滋漢、陳建斌。1995。微波解凍過程中冷凍虱目魚漿過熱熟化現象之改善。食品科學 22:276-283。
12. 陳炯堂、杜宏文。1992。動物膠與陰電性多醣類複合物之流變性與熱性質。食品科學 19:397-405。
13. 陳炯堂。1993。蛋白質與多醣類水溶液之不相溶性。食品科學 20:9-20。
14. 陳仲仁。1996。食品流變學及流變物性儀概論。食品工業月刊 3:8-16
15. 陳俊成。2000。流變學在麵包工業中之應用。食品資訊 175:44-49。