Cybernetics and Systems Analysis

, Volume 49, Issue 5, pp 799–804 | Cite as

A pursuit–evasion problem with a constraint on the distance between objects

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Abstract

A trajectory pursuit–evasion problem is considered under constraints on the velocities of the counteracting objects and on the distance between them. This level of the model study brings the tactical capabilities of designed pilotless aircraft closer to the tactical capabilities of the existing piloted aircraft, which is an important problem of modern aircraft engineering. An approach that allows obtaining exact solutions in specific parametric situations is proposed.

Keywords

pursuit–evasion problem optimal trajectories conflict situations counteracting sides pilotless aircraft 
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References

  1. 1.
    R. Isaacs, Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization (Dover Books on Mathematics), Dover Publications (1999).Google Scholar
  2. 2.
    L. S. Pontryagin, The Maximum Principle in Optimal Control [in Russian], Nauka, Moscow (1989).Google Scholar
  3. 3.
    N. N. Krasovskii, Control of a Dynamic System [in Russian], Nauka, Moscow (1985).Google Scholar
  4. 4.
    B. N. Pshenichnyi, Convex Analysis and Extremum Problems [in Russian], Nauka, Moscow (1980).Google Scholar
  5. 5.
    A. A. Chikrii, Conflict Controlled Processes [in Russian], Naukova Dumka, Kyiv (1992).Google Scholar
  6. 6.
    S. V. Shibaev, “Some informal scenarios of player behavior and equilibrium computation processes in games under incomplete information,” Cybern. Syst. Analysis, 32, No. 1, 125–140 (1996).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    S. F. Krivoi, A. P. Krikovlyuk, I. G. Moroz-Podvorchan, et al., “A problem of pursuit and evasion,” Cybern. Syst. Analysis, 28, No. 3, 445–450 (1992).MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. P. Krikovlyuk and I. G. Moroz-Podvorchan, “A defining feature of the design of one class of specialized control systems,” Upravl. Sist. Mash., No. 1, 63–69 (2011).Google Scholar
  9. 9.
    P. Germain, Cours de Mécanique des Milieux Continus, Masson et Cie, Paris (1973).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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