Abstract
“Homicidal chauffeur” game is one of the most well-known model problems in the theory of differential games. “A car” striving as soon as possible to run over “a pedestrian” – this demonstrative model suggested by R. Isaacs turned out to be appropriate for many applied problems. No less remarkable is the fact that the game is a difficult and interesting object for mathematical investigation. This chapter gives a survey of publications on the homicidal chauffeur problem and its modifications.
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References
Aubin, J.-P.: Viability Theory. Birkhäuser, Basel (1991)
Averbukh, V.L., Ismagilov, T.R., Patsko, V.S., Pykhteev, O.A., Turova, V.L.: Visualization of value function in time-optimal differential games. In: Handlovičová, A., Komorníková, M., Mikula, K., Ševčovič, D. (eds.) Algoritmy 2000, 15th Conference on Scientific Computing, pp. 207–216. Vysoke Tatry – Podbanske, Slovakia (2000)
Bardi, M., Falcone, M., Soravia, P: Numerical methods for pursuit-evasion games via viscosity solutions. In: Bardi, M., Raghavan, T. E. S., Parthasarathy, T. (eds.) Stochastic and Differential Games: Theory and Numerical Methods, Ann. of the Int. Soc. of Dyn. Games, Vol. 4, pp. 105–175. Birkhäuser, Boston (1999)
Bernhard, P., Larrouturou, B.: Étude de la barrière pour un problème de fuite optimale dans le plan. Rapport de recherche. INRIA, Sophia-Antipolis (1989)
Blaquière, A., Gérard, F., Leitmann, G.: Quantitative and Qualitative Differential Games. Academic Press, New York (1969)
Breakwell, J.V., Merz, A.W.: Toward a complete solution of the homicidal chauffeur game. In: Proc. of the 1st Int. Conf. on the Theory and Application of Differential Games, pp. III-1–III-5. Amherst, Massachusetts (1969)
Breitner, M.: The genesis of differential games in light of Isaacs’ contributions. J. Optim. Theory Appl. 124(3), 523–559 (2005)
Cardaliaguet, P., Quincampoix, M., Saint-Pierre, P.: Numerical methods for optimal control and differential games. Ceremade CNRS URA 749, University of Paris - Dauphine (1995)
Cardaliaguet, P., Quincampoix, M., Saint-Pierre, P.: Set-valued numerical analysis for optimal control and differential games. In: Bardi, M., Raghavan, T. E. S., Parthasarathy, T. (eds.) Stochastic and Differential Games: Theory and Numerical Methods, Ann. of the Int. Soc. of Dyn. Games, Vol. 4, pp. 177–247. Birkhäuser, Boston (1999)
Davidovitz, A., Shinar, J.: Two-target game model of an air combat with fire-and-forget all-aspect missiles. J. Optim. Theory Appl. 63(2), 133–165 (1989)
Dubins, L.E.: On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents. Am. J. Math. 79, 497–516 (1957)
Getz, W.M., Pachter, M.: Two-target pursuit-evasion differential games in the plane. J. Optim. Theory Appl. 34(3), 383–403 (1981)
Isaacs, R.: Games of pursuit. Scientific report of the RAND Corporation, Santa Monica (1951)
Isaacs, R.: Differential Games. Wiley, New York (1965)
Krasovskii, N.N.: Control of a Dynamic System. The Minimum Problem of a Guaranteed Result. Nauka, Moscow (1985) (in Russian)
Krasovskii, N.N., Subbotin, A.I.: Game-Theoretical Control Problems. Springer, New York (1988)
Laumond, J.-P. (ed.): Robot Motion Planning and Control. Lect. Notes in Control and Inf. Sci. 229. Springer, New York (1998)
Lewin, J.: Decoy in pursuit-evasion games. PhD thesis, Stanford University (1973)
Lewin, J., Breakwell, J.V.: The surveillance-evasion game of degree. J. Optim. Theory Appl. 16(3–4), 339–353 (1975)
Lewin, J., Olsder, G.J.: Conic surveillance evasion. J. Optim. Theory Appl. 27(1), 107–125 (1979)
Markov, A.A.: Some examples of the solution of a special kind of problem on greatest and least quantities. Soobscenija Charkovskogo Matematiceskogo Obscestva 2, 1(5, 6), 250–276 (1889) (in Russian)
Merz, A.W.: The homicidal chauffeur – a differential game. PhD thesis, Stanford University (1971)
Merz, A.W.: The homicidal chauffeur. AIAA Journal 12(3), 259–260 (1974)
Merz, A.W.: To pursue or to evade – that is the question. J. Guid. Control Dyn. 8(2), 161–166 (1985)
Meyer, A., Breitner, M.H., Kriesell, M.: A pictured memorandum on synthesis phenomena occurring in the homicidal chauffeur game. In: Martin-Herran, G., Zaccour, G. (eds.) Proceedings of the Fifth International ISDG Workshop, pp. 17–32. Int. Soc. of Dyn. Games, Segovia (2005)
Mikhalev, D.K., Ushakov, V.N.: Two algorithms for approximate construction of the set of positional absorption in the game problem of pursuit. Autom. Remote Control 68(11), 2056–2070 (2007)
Mitchell, I.: Application of level set methods to control and reachability problems in continuous and hybrid systems. PhD Thesis, Stanford University (2002)
Olsder, G.J., Breakwell, J.V.: Role determination in aerial dogfight. Int. J. Game Theory 3, 47–66 (1974)
Patsko, V.S., Turova, V.L.: Level sets of the value function in differential games with the homicidal chauffeur dynamics. Int. Game Theory Review 3(1), 67–112 (2001)
Patsko, V.S., Turova, V.L.: Numerical investigation of the value function for the homicidal chauffeur problem with a more agile pursuer. In: Bernhard, P., Gaitsgory, V., Pourtallier, O. (eds.) Advances in Dynamic Games and Their Applications: Analytical and Numerical Developments, Ann. of the Int. Soc. of Dyn. Games, Vol. 10, pp. 231–258. Birkhäuser, Boston (2009)
Raivio, T., Ehtamo, H.: On numerical solution of a class of pursuit-evasion games. In: Filar, J.A., Mizukami, K., Gaitsgory, V. (eds.) Advances in Dynamic Games and Applications, Ann. of the Int. Soc. of Dyn. Games, Vol. 5, pp. 177–192. Birkhäuser, Boston (2000)
Reeds, J.A., Shepp, L.A.: Optimal paths for a car that goes both forwards and backwards. Pac. J. Math. 145(2), 367–393 (1990)
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Patsko, V.S., Turova, V.L. (2011). Homicidal Chauffeur Game: History and Modern Studies. In: Breton, M., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 11. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8089-3_12
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