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Pursuit-Evasion Games

  • Valerii Patsko
  • Sergey Kumkov
  • Varvara Turova
Reference work entry

Abstract

Applied problems whose investigation involves methods of pursuit-evasion differential games are described. The main focus of this chapter is on time-optimal problems close to R. Isaacs’ “homicidal chauffeur” game and to linear differential games of fixed terminal time with J. Shinar’s space interception problem as the major example. These problems are taken because after a change of variables they can be reduced to models with two state variables. This allows us to provide adequate graphical representations of the level sets of the value functions being obtained numerically and emphasize important peculiarities of these sets. Also, other conflict control problems and control problems with uncertainties being extensively investigated nowadays are briefly outlined.

Keywords

Differential game Homicidal chauffeur Space interception Semipermeable curves Barriers Singular surfaces Maximal stable bridge 

Notes

Acknowledgements

The authors are sincerely thankful to E. Bakolas, J. Fisac, V. Glizer, J.-P. Laumond, E.P. Maslov, S. Le Ménec, M. Pachter, H.J. Pesch, L.A. Petrosyan, V. Shaferman, I.I. Shevchenko, T. Shima, P. Tsiotras, and V. Turetsky for their useful consultations.

The authors are grateful to the reviewer for the very helpful remarks, suggestions, and corrections.

The third author acknowledges support by DFG, grant TU427/2-1.

The authors gratefully acknowledge the photographs in Figs. 1 and 2 which were kindly provided by Ellen Sara Isaacs, Antony Willitz Merz, John Alexander Breakwell, and Noa Shinar-Mulder.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.N. N. Krasovskii Institute of Mathematics and MechanicsUral Branch of Russian Academy of SciencesEkaterinburgRussia
  2. 2.Department of MathematicsTechnical University of MunichGarchingGermany

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