New Results About Corners in Differential Games, Including State Constraints

Abstract The way corners occur in even simple two-person, zero-sum differential games is where the main difference lies between these problems and more classical optimal control problems. An attempt at a general theory has been reported earlier. However, new situations arise in the study of specific games, which require a broadening of the theory. Some of these will be presented here, together with a general mean of computing the hypersurfaces of discontinuity. Two simple goal keeping problems will be used as examples to motivate the analysis.