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論文名稱 Title |
以變分法探討具轉向限制之追逐逃逸對局 Variational Approach to Pursuit-Evasion Game with Curvature Constraint |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
98 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2000-05-12 |
繳交日期 Date of Submission |
2000-06-12 |
關鍵字 Keywords |
變分法、轉向限制、追逐逃逸對局 Pursuit-Evasion Game, Variational Approach, Curvature Constraint |
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統計 Statistics |
本論文已被瀏覽 5659 次,被下載 18225 次 The thesis/dissertation has been browsed 5659 times, has been downloaded 18225 times. |
中文摘要 |
在本論文中,我們探討了一種追逐逃逸對局;其中追逐者以作簡單運動的方式移動,同時逃逸者以定速率但具有轉向限制的方式移動,這樣的對局正是一般所謂「殺人司機對局」的逆型式。我們以對局結束當時追逐者與逃逸者間距離的平方作為代價函數。針對這樣的一個零和對局,我們將應用變分法來解決我們的問題,並將就所考慮的各種情況提出一套足以決定對局鞍點與對局解值的演算法則。 |
Abstract |
In this thesis, a pursuit-evasion game, in which the pursuer moves with simple motion whereas the evader moves at a fixed speed but with a curvature constraint, is investigated. The game is the inverse of the usual homicidal chauffeur game. Square of the distance between the pursuer and the evader when the game is terminated is selected as the cost function. To solve such a zero-sum game, the variational approach will be employed to solve the problem. An algorithm will be proposed to determine a saddle point and the value of the game under consideration |
目次 Table of Contents |
誌謝 ........................................ i 中文摘要 .................................... ii ABSTRACT .................................... iii NOMENCLATURE ................................ iv CHAPTER 1 . INTRODUCTION ..................... 1 1.1 Motivation ........................ 1 1.2 Brief Sketch of the Contents ...... 4 CHAPTER 2 . PRELIMINARIES .................... 5 2.1 Brief Review of the Differential Game Theory ............................ 5 2.2 Brief Review of the Variational Approach to Optimal Control Problems ................................... 24 CHAPTER 3 . A PURSUIT-EVASION GAME WITH ONE CURVATURE CONSTRAINT ............. 34 3.1 Introduction and Problem Formulation ................................... 34 3.2 Analysis and Main Results ......... 38 3.3 Illustrative Examples ............. 55 CHAPTER 4. DISCUSSIONS AND CONCLUSIONS ...... 67 REFERENCES .................................. 76 APPENDIX A. The Program for Simulating the Case when Both Players Play Optimally .................................. 84 B. The Program for Simulating the Case when Only the Plays Optimally .................................. 89 C. The Program for Simulating the Case when Only the Pursuers Plays Optimally ........................ 94 |
參考文獻 References |
[Ard.1] M. Ardema and N. Rajan, An approach to three-dimensional aircraft pursuit-evasion, Computer Mathematics Applications, Vol. 13, pp.97-110, 1987. [Ber.1] L. Berkovitz, A variational approach to differential games, Annals of Mathematics Study, Vol. 52, pp. 127-174, 1964. [Bor.1] P. Borowko and W. Rzymowski, On the game of two cars, Journal of Optimization Theory and Applications, Vol. 44, No. 3, pp. 381-396, 1984. [Bre.1] J. V. Breakwell, Pursuit of a faster evader, The Theory and Application of Differential games, J. D. Grote, ed., Vol. 13, Dordrecht, Holland, 1974. [Bry.1] A. E. Bryson and Jr. Y. C. Ho, Applied Optimal Control: Optimization, Estimation, and Control, Blaisdell, M.A, 1969. [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. [Coc.1] E.J. Cockayne, Plane pursuit with curvature constraints, SIAM Journal on Applied Mathematics, Vol. 15, pp. 1511-1516, 1967. [Coc.2] E.J. Cockayne and G.W.C. Hall, Plane motion of a particle subject to curvature constraints, SIAM Journal of Control, Vol. 13, pp. 197-220, 1975. [Fri.1] A. Friedman, Differential Games, John Wiley & Sons, New York, 1971. [Get.1] W. M. Getz and M. Pachter, Capturability in a two-target game of two cars, Journal of Guidance and Control, Vol. 4, No. 1, pp. 15-21, 1981. [Get.2] W. M. Getz and M. Pachter, Two-target pursuit-evasion differential games in the plane, Journal of Optimization Theory and Applications, Vol. 34, No. 3, pp. 383-403, 1981. [Gup.1] N. K. Gupta, An overview of differential games, Control and Dynamic Systems: Advanced in Theory and Applications, C. T. Leondes, ed., Vol. 17, Academic Press, New York, 1981. [Haj.1] O. Hajek, 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, No. 2, pp. 157-167, 1993. [Hsi.2] K. H. Hsia and J. G. Hsieh, Fuzzy differential game of guarding a territory: Different speed case, First International Conference on Fuzzy Theory and Technology, Control and Decision, Durham, North Carolina, 1992. [Hsi.3] 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.4] K. H. Hsia, J. G. Hsieh, H. J. Chu and L. W. Chen, Some results of fuzzy differential game of guarding a movable territory, Proceeding of the First National Symposium on Fuzzy Set Theory and Applications, Hsing-Chu, Taiwan, pp. 149-156, 1993. [Hsi.5] K. H. Hsia, Research on the fuzzy differential game problems, Ph.D. Dissertation, National Sun Yat-sen University, Kaohsiung, Taiwan, 1994. [Hsi.6] 謝哲光、夏郭賢、朱弘仁,模糊微分對局簡介,全華科技圖 書股份有限公司,台北市,1993。 [Hsi.7] 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 and Sons, New York, 1965. [Isa.2] R. Isaacs, The past and some bits of the future, The Theory and Application of Differential games, J. D. Grote, ed., Vol. 13, Dordrecht, Holland, 1974. [Kal.1] N. J. Kalton, Differential games of survival, The Theory and Application of Differential games, J. D. Grote, ed., Vol. 13, Dordrecht, Holland, 1974. [Kas.1] B. Kaskosz, On a nonlinear evasion problem, SIAM Journal on Control and Optimization, Vol. 15, No. 4, pp. 661-673, 1977. [Kir.1] D.E. Kirk, Optimal Control Theory: An Introduction, Prentice- Hall, New Jersey, 1970. [Lee.1] Y. S. Lee, K. H. Hsia and J. G. Hsieh, A reasonable strategy based on similarity measure for a reasoning differential game, Proceeding of International Conference on Automation Technology, Taipei, Taiwan, accepted, 2000. [Lee.2] Y. S. Lee, K. H. Hsia and J. G. Hsieh, A fuzzy reasoning differential game, Proceeding of the International Fuzzy Systems Association World Congress, Taipei, Taiwan, Vol. 2, pp. 772-776, 1999. [Lei.1] G. Leitmann, The Calculus of Variations and Optimal Control: An Introduction, Plenum, New York, 1983. [Leo.1] C. T. Leondes, Control and Dynamic Systems: Advanced in Theory and Applications, Vol. 17, Academic Press, New York, 1981. [Mer.1] A. W. Merz, The homicidal chauffeur, a differential game, Ph.D. Dissertation, Stanford University, Stanford, U.S.A., 1971. [Mer.2] A. W. Merz, The game of two identical cars, Journal of Optimization Theory and Applications, Vol. 9, No. 5, pp. 324- 343, 1972. [Mil.1] T. Miloh, A note on three-dimensional pursuit-evasion game with bounded curvature, IEEE Transactions on Automatic Control, Vol. 27, No. 3, pp. 739-741, 1982. [Pac.1] M. Pachter, Simple-motion pursuit-evasion in the half plane, Computers and Mathematics with Applications, Vol. 13, pp. 69- 82, 1987. [Pac.2] M. Pachter and Y. Yavin, Simple-motion pursuit-evasion games- part I: stroboscopic strategies in collision course ..., Journal of Optimization Theory and Applications, Vol. 51, pp. 95-127, 1986. [Pac.3] M. Pachter and Y. Yavin, Simple-motion pursuit-evasion differential games-part II: optimal evasion from ..., Journal of Optimization Theory and Applications, Vol. 51, pp. 129-159, 1986. [Pet.1] L. A. Petrosjan, Differential Games of Pursuit, World Scientific, Singapore, New Jersey, London, HongKong, 1993. [Pra.1] U. R. Prasad, N. Rajan and N. J. Rao, Planar pursuit-evasion with variable speeds: extremal trajectory maps, Journal of Optimization Theory and Applications, Vol. 33, pp. 401-418, 1981. [Pra.2] U. R. Prasad and N. Rajan, Aircraft pursuit-evasion problems with variable speeds, Computers and Mathematics with Applications, Vol. 13, pp. 111-122, 1987. [Rad.1] J. E. Rader, Use of parameter optimization methods to determine the existence of game theoretic saddle points, Control and Dynamic Systems: Advanced in Theory and Applications, C. T. Leondes, ed., Vol. 17, Academic Press, New York, 1981. [Rag.1] Raghavan, T. E. S., T. S. Ferguson and O. J. Vrieze, eds. Stochastic games and related topics, Kluwer Academic Press, Massachusetts, 1989. [Raj.1] N. Rajan, U. R. Prasad and N. J. Rao, Pursuit-evasion of two aircraft in a horizontal plane, Journal of Guidance and Control, Vol. 3, No. 3, pp. 261-267, 1980. [Raj.2] N. Rajan, U. R. Prasad and N. J. Rao, Planar pursuit-evasion with variable speeds: barrier sections, Journal of Optimization Theory and Applications, Vol. 33, pp. 419-432, 1981. [Rod.1] E. Y. Rodin, A pursuit-evasion bibliography - version 2, Computers and Mathematics with Applications, Vol. 18, No. 1-3, pp. 245-320, 1989. [Rub.1] G. T. Rublein, On pursuit with curvature constraints, SIAM Journal of Control, Vol. 10, No. 1, pp. 37-39, 1972. [Shi.1] J. Shinar, Solution techniques for realistic pursuit-evasion games, Control and Dynamic Systems: Advanced in Theory and Applications, C. T. Leondes, ed., Vol. 17, Academic Press, New York, 1981. [Sta.1] H. Stalford, Sufficient conditions for optimal control with state and control constraints, Journal of Optimization Theory and Applications, Vol. 7, No. 2, pp. 118-135, 1971. [Sta.2] H. Stalford, Sufficient conditions for optimality in two-person zero-sum differential games with state and strategy constraints, Journal of Mathematical Analysis and Applications, Vol. 33, pp. 650-654, 1971. [Yav.1] Y. Yavin and R. de Villiers, The game of two cars with a containment probability as a cost function: the case of variable speed, Computer Mathematics Applications, Vol. 18, pp. 61-67, 1989. [Yav.2] Y. Yavin and R. de Villiers, Proportional navigation and the game of two cars: the case of a pursuer with variable speed, Computer and Mathematics Applications, Vol. 18, pp. 69-75, 1989. |
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