Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

Abstract

The theory of nonzero sum differential games (NZSDG) is extended for a class of problems in which the nonlinear system equations have bounded control variables appearing linearly. For terminal cost functions this class of problems is shown to exhibit 'bang-bang' type control laws with the possibility of singular controls. A condition is derived to test for continuity of the influence functions when controls switch from a nonsingular to a singular control on singular surfaces. Two generalized forms of the transversality conditions are derived for NZSDG theory extending results of Dreyfus and Isaacs. NZSDG theory is shown to be useful in modeling combat problems in which the goals of the players are not diametrically opposed. A two player and three player penetrator-interceptor problem are presented as a NZSDG. Numerical solutions for a totally singular problem are carried out to illustrate application and a typical solution.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1971
Accession Number
ADA007879

Entities

People

  • Anthony L. Leatham

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Air Force
  • Aircrafts
  • Algorithms
  • Boundary Value Problems
  • Differential Equations
  • Engineering
  • Equations
  • Equations Of State
  • Flight Paths
  • Game Theory
  • Line Of Sight
  • Nonlinear Systems
  • Partial Differential Equations
  • Supersonic Aircraft
  • Systems Engineering
  • Time Intervals
  • Trajectories

Fields of Study

  • Mathematics

Readers

  • Aerospace Propulsion Engineering.
  • Calculus or Mathematical Analysis
  • Operations Research