Numerical study of differential games with the homicidal chauffeur dynamics (Q2710186)

The authors present an algorithm for computing the level sets of the value function of three homicidal chauffeur differential games on the plane. The algorithm uses a classical backward construction of level sets, but exploits a specific analysis of the structure of the roots of the Hamltonian of the game to examine the possibility of appearance of `holes' in the solvability set of the minimizing player. It is shown why such holes cannot appear in the classical version of the game, and how they appear in the richer variants considered, for various terminal sets (in particular rectangles, besides the usual circles). The two variants are an `acoustic' version where the evader must reduce speed when the pursuer comes close (`not to be heard by him'); and a `conic surveillance' game where the pursuer wants to keep the evader `in sight' inside a pointed cone.