Families of semipermeable curves in differential games with the homicidal chauffeur dynamics

摘要

Families of semipermeable curves in differential games with the homicidal chauffeur dynamics are studied both from the theoretical and computational points of view. The knowledge of such families is very useful for the investigation of time-optimal problems because semipermeable curves bound the solvability set and can also appear as barrier lines on which the value function is discontinuous. Three variants of differential games with the homicidal chauffeur dynamics are considered. Results of the computation of level sets of the value function for these games are discussed.