Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Boundary arcs for a class of differential games


The behavior of boundary arcs of the attainable set is discussed for a class of differential games, and first-order necessary conditions are obtained. The method is a simple extension of that used by Hestenes (Ref. 1) in relating the behavior of boundary arcs for optimal control problems to the maximum principle.

This is a preview of subscription content, log in to check access.


  1. 1.

    Hestenes, M. R.,Calculus of Variations and Optimal Control Theory, John Wiley and Sons, New York, 1967.

  2. 2.

    Berkovitz, L. D.,A Variational Approach to Differential Games, Advances in Game Theory, Edited by M. Dresher, L. S. Shapley, and A. W. Tucker, Annals of Mathematics, Study 52, Princeton University Press, Princeton, New Jersey, 1964.

  3. 3.

    Berkovitz, L. D.,Necessary Conditions for Optimal Control Strategies in a Class of Differential Games and Control Problems, SIAM Journal on Control, Vol. 5, No. 1, 1967.

Download references

Author information

Additional information

Portions of this work were sponsored by the Douglas Aircraft Company, Independent Research and Development Fund No. 80421-021/39051.

Communicated by M. R. Hestenes

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Guinn, T. Boundary arcs for a class of differential games. J Optim Theory Appl 2, 293–315 (1968).

Download citation


  • Control Problem
  • Maximum Principle
  • Optimal Control Problem
  • Differential Game
  • Simple Extension