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On the existence of value in the Varaiya-Lin sense in differential games of pursuit and evasion

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Abstract

This paper is strictly related to Ref. 1. A pursuit-evasion game described in part by the system\(\dot x = f_1 (t,x,u)\) and\(\dot y = f_2 (t,y,v)\) is considered. The state variablesx andy are restricted, in the sense that (x(t),t) ∈N 1 and (y(t),t) ∈N 2. The existence of a value in the sense of Varaiya and Lin is proved under the assumption that the sets of all admissible trajectories for the two players are compact and the lower value is not greater than the upper value.

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References

  1. 1.

    Varaiya, P. P., andLin, J.,Existence of Saddle Points in Differential Games, SIAM Journal on Control, Vol. 7, pp. 142–157, 1969.

  2. 2.

    Zaremba, L. S.,The Existence of Value in Pursuit-Evasion Games with Restricted Phase Coordinates, Journal of Optimization Theory and Applications (to appear).

  3. 3.

    Varaiya, P. P.,On the Existence of Solutions to a Differential Game, SIAM Journal on Control, Vol. 5, pp. 153–161, 1967.

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Communicated by P. Varaiya

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Zaremba, L.S. On the existence of value in the Varaiya-Lin sense in differential games of pursuit and evasion. J Optim Theory Appl 29, 135–145 (1979). https://doi.org/10.1007/BF00932640

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Key Words

  • Pursuit-evasion games
  • strategy
  • lower value
  • upper value