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Differential games with parameters

  • J. Doležal
Differential Games
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 22)

Abstract

In addition to the classical formulation of many-player differential games one of the players, say the first, can choose values of certain parameters to further decrease his pay-off functional with respect to its equilibrium (Nash) value. Such action causes clearly the changes in pay-off functionals of the remaining players, which can be both positive and negative, in general. For this problem a set of necessary optimality conditions is presented, which enable to determine not only equilibrium strategies of all participating players, but also optimal parameters. Based on these conditions a gradient-type algorithm is suggested, the use of which is illustrated on examples.

Keywords

Differential Game Optimal Control Theory Quasilinearization Method Differential Game Problem Iterative Numerical Technique 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Ahmed, N.U., Georganas, N.D.: On optimal parameter selections. IEEE Trans. on Automatic Control AC-18 (1973), 313–314.Google Scholar
  2. 2.
    Boltjanskij, V.G.: Mathematical Methods of Optimal Control. Nauka, Moscow 1969. In Russian.Google Scholar
  3. 3.
    Bryson, A.E., Ho, Y.C.: Applied Optimal Control. Ginn, Waltham 1969.Google Scholar
  4. 4.
    Case, J.H.: Toward a theory of many player differential games. SIAM J. Control 7 (1969), 179–197.Google Scholar
  5. 5.
    Doležal, J.: A Modified Quasilinearization Method for Discrete Two-Point Boundary-Value Problems. Res. Report No. 639, ÚTIA ČSAV 1977.Google Scholar
  6. 6.
    Doležal, J.: Optimal parameter estimation in two-player zero-sum differential games. “Trans. 8th Prague Conf. on Infor. Theory, Statis. Dec. Functions, Random Proc.”, Driml, M. (ed.), Vol. A, Academia, Prague 1978, 143–156.Google Scholar
  7. 7.
    Doležal, J.: A gradient-type algorithm for the numerical solution of two-player zero-sum differential games. Kybernetika 14 (1978), 429–446.Google Scholar
  8. 8.
    Doležal, J.: Parameter optimization for two-player zero-sum differential games. Trans. of the ASME 101 (1979), Ser. G.Google Scholar
  9. 9.
    Doležal, J.: Parameter optimization in nonzero-sum differential games. Kybernetika 16 (1980). To appear.Google Scholar
  10. 10.
    Doležal, J., Černý, P.: The application of optimal control methods to the determination of multifunctional catalyst. Automatizace 21 (1978), 1–8. In Czech.Google Scholar
  11. 11.
    Doležal, J., Thoma, M.: On the numerical solution of N-player non-zero-sum differential games via Nash solution concept. Problems of Control and Information Theory 8 (1979).Google Scholar
  12. 12.
    Miele, A.: Recent advances in gradient algorithms for optimal control problems. JOTA 17 (1975), 361–430.Google Scholar
  13. 13.
    Gonzales, S., Miele, A.: Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions. JOTA 26 (1978), 395–425.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • J. Doležal
    • 1
  1. 1.Institute of Information Theory and AutomationCzechoslovak Academy of SciencesPragueCzechoslovakia

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