Advertisement

Analytical study of a case of the homicidal chauffeur game problem

  • Christian Marchal
Theory Of Games
Part of the Lecture Notes in Computer Science book series (LNCS, volume 27)

Abstract

This paper is a shorter presentation of the Ref 11 presented at the IFIP conference.

The analytical study of the homicidal chauffeur game problem is developed with the help of the Pontryagin's theory of optimization and its generalization to deterministic two-player zero-sum differential games.

Different phenomena are encountered : universal line, disperal line, barrier, equivocal line etc... and their equations or at least their differential equations are given. The study is not complete because its end is very complicated but is shows at least how a systematic construction of the "separatrix" can solve the problem and help to understand it.

Keywords

Optimality Theory Playing Space Differential Game Extremal Trajectory Dispersal Line 
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.

References

  1. [1]
    ISAACS, R. — "Differential games", Wiley, New-York, (1965).Google Scholar
  2. [2]
    BRYSON, A.E; HO, Y.C. — "Applied optimal control" Blaisdell Publisching Co, Waltham, Mass, (1969).Google Scholar
  3. [3]
    BREAKWELL, J.V; MERZ A.W. — "Toward a complete solution of the homicidal chauffeur game" Proceedings of the first international conference on the theory and applications of differential games. Amherst, Mass, (1969), pp III 1–III 5.Google Scholar
  4. [4]
    BREAKWELL, J.V — "Some differential games with interesting discontinuities" Navy Workshop on Differential games, Aug. 3 (1973, U.S Naval Academy, Annapolis Md.).Google Scholar
  5. [5]
    BERNHARD P. — "Linear Pursuit-Evasion games and the Isotropic Rocket" SUDAAR no 413, Ph D thesis, Dec. 1970, Stanford University Center for Systems Research, Stanford, California.Google Scholar
  6. [6]
    MERZ A.W. — "The homicidal chauffeur: A differential game" SUDAAR no 418, Ph D. thesis, March 1971, Stanford University Center for Systems Research, Stanford California.Google Scholar
  7. [7]
    MERZ A.W. — "The homicidal chauffeur" AIAA Journal Vol 12, no 3, March 1974, pp 259–260.Google Scholar
  8. [8]
    MARCHAL C. — "Generalization of the optimality theory of Pontryagin to deterministic two-player zero-sum differential games". Communication présentée à la 5ème Conférence IFIP sur les Techniques d'Optimisation — Rome 7.11 mai 1973 — ONERA T.P. no 1233 (1973).Google Scholar
  9. [9]
    FRIEDMAN A. — "Differential Games" Wiley Interscience, a Division of John Wiley and Sons, Inc.-New-York-London-Sydney-Toronto (1971).Google Scholar
  10. [10]
    KUHN H.W., SZEGO G.P. — "Differential games and related topics". North Holland Publishing company-Amsterdam-London (1971).Google Scholar
  11. [11]
    MARCHAL C. — "Analitycal study of the homicidal chauffeur game problem" Paper presented at the IFIP Technical Conference on Optimization Techniques — Novosibirsk — USSR — 1.7 July 1974 — Also T.P. ONERA no 1385 (1974).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Christian Marchal
    • 1
  1. 1.OneraChatillonFrance

Personalised recommendations