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Tytuł książki

Method of construction of the evasion strategy for differential games with many pursuers

Autorzy

Witold Rzymowski

Seria

Rozprawy Matematyczne tom/nr w serii: 247 wydano: 1986

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Pełne teksty:
rm24701.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS
Introduction...........................................................................5
1. Preliminaries.....................................................................6
 1.1. Notation........................................................................6
 1.2. Control systems. Strategies..........................................7
2. Main lemma......................................................................9
3. Avoidance of many pursuers..........................................14
 3.1. First step....................................................................16
 3.2. Continuation...............................................................22
4. Evasion along each trajectory........................................27
 4.1. Some general criteria.................................................30
 4.2. Some special examples..............................................33
  4.2.1. The homicidal Chauffeur game..............................34
  4.2.2. The game of 1+n cars............................................36
5. Differential games of many evaders and pursuers.........37
 5.1. General example........................................................37
 5.2. A squadron of ships amidst iceberges........................38
6. On evasion games with incomplete information..............39
7. Final remarks.................................................................41
References........................................................................42

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 247

Liczba stron

43

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCXLVII

Daty

wydano
1986

Twórcy

autor
Witold Rzymowski

Bibliografia

  • [1] P. Borówko, Application of a certain method of approximation to the theory of orientor fields and differential games. J. Differ. Eqs. 48 (1983), 17-34.
  • [2] P. Borówko, W. Rzymowski, On the game of two cars, J. Optimization Theory and Applications, to appear.
  • [3] J. V. Breakwell, A. W. Merz, Minimum required capture radius in a coplanar model of the aerial combat problem, AIAA. J. 15 (1977), 1089-1094.
  • [4] F. L. Černousko, A. A. Melikian, Game problems of control and search (in Russian), Nauka, Moscow 1978.
  • [5] A. A. Čikrij, Sufficient conditions of evasion for nonlinear games with many participants (in Russian), Tekhn. Kibernetika 6 (1978), 14-21.
  • [6] A. A. Čikrij, Nonlinear differential evasion games. Soviet. Math. Dokl. 20 (1979). 591- 595.
  • [7] A. A. Čikrij, I. S. Rappoport, On the linear pursuit problem (in Russian), Kibernetika 3 (1978), 86-92.
  • [8] J. Flynn, Pursuit in the circle: lion versus man, in: Differential games and control theory, Eds. E. Roxin, Pan-Tai Liu, R. L. Sternberg, Lecture Notes in Pure and Applied Mathematics 10,-Marcel Dekker Inc., New York 1974, 99-124.
  • [9] A. Friedman, Computation of saddle points for differential games of pursuit and evasion, Archive for Rational Mechanics and Analysis 40 (1971), 79-119.
  • [10] A. Friedman, Differential Games, Viley-Interscience, New York London-Sydney Toronto 1971.
  • [11] P. B. Gusiatnikov, Three dimensional evasion problem for games with many pursuers (in Russian), Izv. Akad. Nauk USSR, Tekhn. Kibernetika 5 (1976), 30-36.
  • [12] P. B. Gusiatnikov, Differential evasion game with m pursuers (in Russian), ibidem 6 (1978). 22 32.
  • [13] P. B. Gusiatnikov, J. S. Lediajev, A. W. Mezencev, Differential evasion games with delay of information (in Russian), PMM 43 (1979), 195-203.
  • [14] R. Isaacs, Differential games. Wiley, New York 1965.
  • [15] B. Kaśkosz, On a nonlinear evasion problem, SIAM J. Control Optimization 15 (1977), 611-673.
  • [16] N. N. Krasovski, On differential evolution systems (in Russian), PMM 41 (1977), 774-782.
  • [17] N. N. Krasovski, A. I. Subbotin, Positional differential games (in Russian), Nauka, Moscow 1974.
  • [18] J. Levin, Lion and man - revisited, to appear.
  • [19] J. Macki, A. Strauss, Introduction to optimal control theory, Springer-Verlag, New York-Heidelberg-Berlin 1982.
  • [20] V. V. Ostapenko, On the nonlinear evasion problem (in Russian) Kibernetika 4 (1978), 106-112.
  • [21] P. A. Petrosjan, Differential pursuit games (in Russian), Izd. Leningr. Univ., Leningrad 1977.
  • [22] L. S. Pontrjagin, Linear differential games, SIAM J. Control Optimization 12 (1974), 262-267.
  • [23] L. S. Pontrjagin, E. F. Miscenko, Evasion problem for linear differential games (in Russian), Diff. Uravnenija 7 (1971), 436-445.
  • [24] B. N. Pšeničny, ε-strategies in differential games, In Topics in Differential Games, Ed. A. Blaquiere, North Holland- Amer. Elselvier, New York 1973, 44-99.
  • [25] B. N. Pšeničny, On the evasion problem (in Russian), K.ibernetika 4 (1975), 120-127.
  • [26] B. N. Pšeničny, Simple pursuit games with many pursuers (in Russian), ibidem 3 (1976), 145-146.
  • [27] Cz. Rydz-Nardzewski, A theory of pursuit and evasion, Adv. in game theory, Ann. Math. Studies, Eds. M. Dresher, L. S. Shapley and A. W. Tucker, Univ. Press, Princeton 1964.
  • [28] W. Rzymowski, Two consequences of one solution of an evasion problem (in Russian). Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 155-159.
  • [29] W. Rzymowski, On the game of 1 + n cars, J. Math. Analys. Appl. 99 (1984), 109-122.
  • [30] W. Rzymowski, Evasion along each trajectory in differential games with many pursuers, J. Differ. Eqs. (to appear).
  • [31] S. I. Tarlinski, On a nonlinear differential games with many pursuers (in Russian), Dokl. Akad. Nauk USSR 230 (1976), 534-537.
  • [32] G. W. Tomski, Problem of pursuit-evasion for quasi-dynamical systems (in Russian), PMM 42 (1978), 219- 227.
  • [33] P. Varaiya, The existence of solutions to a differential game, SIAM J. Control Optimization 5 (1967), 153-162.
  • [34] T. L. Vincent, Collision avoidance at sea, in the Proceedings of a Workshop Held in Enschede, Eds. P. Hagedorn, H. W. Knobloch and G. J. Olsder. Lecture Notes in Control and Information Sciences 3 (1977), 205-221.
  • [35] V. L. Zak, On an evasion problem from many pursuers (in Russian), PMM 43 (1979), 456 465.
  • [36] V. L. Zak, Evasion of inert object from many pursuers (in Russian), Izv. Akad. Nauk USSR, Tekhn. Kibernetika 1 (1980), 26- 31.
  • [37] V. L. Zak, A piecewise program strategy of evasion from many pursuers (in Russian), Institute for Problems in Mechanics, Moscow 1982, preprint.
  • [38] L. S. Zaremba, On the existence of value in the Varaiya-Lin sense in differential games of pursuit and evasion, J. Optimiz. Theory and Applications 29 (1979), 135-145.
  • [39] M. I. Zelikin, A certain differential game with incomplete information (in Russian), Dokl. Akad. Nauk USSR 202 (1972), 998-1000.

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ISBN
83-01-06574-5
ISSN
0012-3862

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