FORMAL SOLUTIONS FOR A CLASS OF STOCHASTIC PURSUIT-EVASION GAMES

Abstract

A class of differential pursuit-evasion games is examined in which the dynamics are linear and perturbed by additive white Gaussian noise, the performance index is quadratic, and both players receive measurements perturbed independently by additive white Gaussian noise. A direct application of the saddle point condition is used formally to characterize linear minimax solutions in terms of a system of implicit integro-differential equations, which appears to be more complicated than the ordinary kind of two point boundary value problem. It is also shown that games of this type posses a 'certainty-coincidence' property, meaning that their behavior coincides with that of corresponding deterministic games in the event that all noise values are zero. This property is used to decompose the minimax strategies into sums of a certainty-equivalent term and error terms.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1968
Accession Number
AD0679232

Entities

People

  • W. W. Willman

Organizations

  • Harvard University

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Calculus Of Variations
  • Computations
  • Difference Equations
  • Differential Equations
  • Dynamics
  • Engineering
  • Equations
  • Kalman Filters
  • Mathematical Analysis
  • Mathematical Filters
  • Measurement
  • Military Research
  • Noise
  • Physics
  • Random Variables

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Game Theory.