Some problems in the theory of differential pursuit games in systems with distributed parameters

A game with dynamics described by partial differential equations is considered. The equations of the players are additively represented on the right-hand side and are subject to integral or pointwise restrictions. The goal of the first player, who is informed of the instantaneous value of the contro...

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Published in:Journal of applied mathematics and mechanics Vol. 59; no. 6; pp. 935 - 940
Main Author: Tukhtasinov, M
Format: Journal Article
Language:English
Published: Elsevier Ltd 1995
ISSN:0021-8928
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Abstract A game with dynamics described by partial differential equations is considered. The equations of the players are additively represented on the right-hand side and are subject to integral or pointwise restrictions. The goal of the first player, who is informed of the instantaneous value of the control of his partner, is to bring the system into an unperturbed state. To solve the problem the decomposition method developed in [1] for a controlled system (with one player) is used. Three combinations of restrictions on the players are considered. In all cases the control of the first player is presented explicitly. The main complication, compared with the problem considered previously [1] is that this control consists of two terms estimated in different norms.
AbstractList A game with dynamics described by partial differential equations is considered. The equations of the players are additively represented on the right-hand side and are subject to integral or pointwise restrictions. The goal of the first player, who is informed of the instantaneous value of the control of his partner, is to bring the system into an unperturbed state. To solve the problem the decomposition method developed in [1] for a controlled system (with one player) is used. Three combinations of restrictions on the players are considered. In all cases the control of the first player is presented explicitly. The main complication, compared with the problem considered previously [1] is that this control consists of two terms estimated in different norms.
Author Tukhtasinov, M
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References Chernous'ko (BIB1) 1992; 56
Nikol'skii (BIB5) 1975
Mikhlin (BIB3) 1977
Avdonin, Ivanov (BIB4) 1989
Satimov (BIB2) 1981; 29
Satimov (10.1016/0021-8928(95)00126-3_BIB2) 1981; 29
Mikhlin (10.1016/0021-8928(95)00126-3_BIB3) 1977
Nikol'skii (10.1016/0021-8928(95)00126-3_BIB5) 1975
Chernous'ko (10.1016/0021-8928(95)00126-3_BIB1) 1992; 56
Avdonin (10.1016/0021-8928(95)00126-3_BIB4) 1989
References_xml – start-page: 59
  year: 1975
  end-page: 66
  ident: BIB5
  article-title: On the pursuit problem with various constraints on the controls of the pursuer and evader
  publication-title: Theory of Optimal Solutions
– volume: 56
  start-page: 810
  year: 1992
  end-page: 826
  ident: BIB1
  article-title: Constrained controls in systems with distributed parameters
  publication-title: Prikl. Mat. Mekh.
– year: 1977
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  article-title: Linear Partial Differential Equations
– volume: 29
  start-page: 455
  year: 1981
  end-page: 476
  ident: BIB2
  article-title: On pursuit and evasion problems in differential games
  publication-title: Mat. Zametki
– year: 1989
  ident: BIB4
  article-title: The Controllability of Systems with Distributed Parameters and Families of Exponents
– start-page: 59
  year: 1975
  ident: 10.1016/0021-8928(95)00126-3_BIB5
  article-title: On the pursuit problem with various constraints on the controls of the pursuer and evader
– volume: 56
  start-page: 810
  issue: 5
  year: 1992
  ident: 10.1016/0021-8928(95)00126-3_BIB1
  article-title: Constrained controls in systems with distributed parameters
  publication-title: Prikl. Mat. Mekh.
– year: 1977
  ident: 10.1016/0021-8928(95)00126-3_BIB3
– year: 1989
  ident: 10.1016/0021-8928(95)00126-3_BIB4
– volume: 29
  start-page: 455
  issue: 3
  year: 1981
  ident: 10.1016/0021-8928(95)00126-3_BIB2
  article-title: On pursuit and evasion problems in differential games
  publication-title: Mat. Zametki
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