The Classical Homicidal Chauffeur Game
Tóm tắt
The Homicidal Chauffeur differential game is often mentioned in the literature, but the game’s complete solution is not readily available. In this work, the complete solution process of the Homicidal Chauffeur differential game is illustrated for the parameter range in the heart of the speed ratio-capture radius parameter space initially investigated by Isaacs, and referred to by Breakwell and Merz as the classical Homicidal Chauffeur differential game. Some salient features of the solution of this foundational differential game are highlighted, and some popular misconceptions are dispelled. This tutorial paper fills a gap in the literature on pursuit-evasion differential games.
Tài liệu tham khảo
Barron EN, Jensen R (1986) The Pontryagin maximum principle from dynamic programming and viscosity solutions to first-order partial differential equations. Trans Am Math Soc 298:635–641
Bernhard P (1992) Differential games: lecture notes on the Isaacs–Breakwell theory. Summer School on Differential Games, Cagliari
Boltyanskii VG (1971) Mathematical methods of optimal control. Holt, Rinehart, and Winston, New York
Coates S, Pachter M, Murphey R (2017) Analysis of Example 10.6.1 in Isaacs’ Book. Unpublished
Coates S, Pachter M, Murphey R (2017) Optimal control of a Dubins car with a capture set and the homicidal chauffeur differential game. Presented at the 57th Israel annual conference on aerospace sciences, Tel Aviv & Haifa and in the proceedings of the 20th World Congress of IFAC, Toulouse, France, pp 5247–5252
Dubins LE (1957) On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am J Math 79(3):497–516
Isaacs R (1965) Differential games: a mathematical theory with applications to warfare and pursuit, control and optimization. Wiley, New York, pp 297–304
Kumkov SS, Le Menec S, Patsko VS (2017) Zero-sum pursuit-evasion differential games with many objects: survey of publications. Dyn Games Appl 7(4):609–633. https://doi.org/10.1007/s13235-016-0209-z
Lewin J (1994) Differential games: theory and methods for solving game problem with singular surfaces. Springer, London, pp 188–194
Merz AW (1971) The Homicidal Chauffeur—a differential game. Ph.D. Dissertation, Stanford University
Merz AW (1974) The Homicidal Chauffeur. AIAA J 12(3):259–260
Patsko VS, Turova VL (2009) Homicidal Chauffeur games: history and modern studies. Scientific report. Institute of Mathematics and Mechanics, Ekaterinburg
Pontryagin LS (1987) Mathematical theory of optimal processes. CRC Press, New York