Cybernetics and Systems Analysis

, Volume 45, Issue 2, pp 297–302 | Cite as

Pursuit problem in distributed control systems

Systems Analysis

A pursuit problem in distributed parabolic control systems without mixed derivatives with variable coefficients is considered. The finite-difference method is used to solve this problem. Necessary conditions for the termination of a pursuit are obtained.


pursuit pursuer evader terminal set pursuit control evasion control 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).Google Scholar
  2. 2.
    A. G. Butkovskii, Control Methods for Distributed-Parameter Systems [in Russian], Nauka, Moscow (1975).Google Scholar
  3. 3.
    V. A. Il’in, “Boundary control of the string oscillation process at two ends,” Dokl. AN SSSR, 369, No. 5, 592–596 (1999).Google Scholar
  4. 4.
    V. A. Il’in and V. V. Tikhomirov, “Wave equation with boundary control at two ends and the problem of complete damping of the oscillating process,” Dif. Uravneniya, 35, No. 5, 692–704 (1999).MathSciNetGoogle Scholar
  5. 5.
    Yu. S. Osipov and S. P. Okhezin, “On the theory of differential games in parabolic systems,” Dokl. AN SSSR, 226, No. 6, 1267–1270 (1976).Google Scholar
  6. 6.
    A. I. Korotkii and Yu. S. Osipov, “Approximation in problems of position control of parabolic systems,” Prikl. Mat. Mekh., 42, No. 4, 599–605 (1978).MathSciNetGoogle Scholar
  7. 7.
    N. Satimov and M. Sh. Mamatov, “A class of linear differential and discrete games between groups of pursuers and evaders,” Dif. Uravneniya, 26, No. 9, 1541–1551 (1990).MATHMathSciNetGoogle Scholar
  8. 8.
    N. Satimov and M. Tukhtasinov, “On some game problems for first-order controlled evolution equations,” Dif. Uravneniya, 41, No. 8, 1114–1121 (2005).MathSciNetGoogle Scholar
  9. 9.
    M. Tukhtasinov, “Some problems in the theory of differential pursuit games in systems with distributed parameters,” Prikl. Mat. Mekh., 59, No. 6, 979–984 (1995).MathSciNetGoogle Scholar
  10. 10.
    M. S. Mamatov, “On a pursuit game problem described by partial differential equations,” in: Proc. Intern. Conf. “Differential Equations, Function Theory, and Applications,” Novosibirsk (2007), pp. 223–224.Google Scholar
  11. 11.
    M. S. Mamatov and M. Tukhtasinov, “Application of the finite-difference method to pursuit problems in systems with distributed parameters,” in: Proc. Intern. Conf. “Information-Mathematical Technologies in Economy, Engineering, and Education,” Yekaterinburg (2007), pp. 36–39.Google Scholar
  12. 12.
    G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow (1989).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.National University of UzbekistanTashkentUzbekistan

Personalised recommendations