Value-functions for Differential Games and Control Systems with Discontinuous Terminal Cost

Differential Games and Zubov's Method

“…One of the main questions in differential games is whether V + and V − coincide, in which case one says that there exists a value for the game. For the case of nonanticipative strategies this question is investigated for instance in [19], [3], [5], [6], [14], [15], [17], [30], [31]. Typically, Isaacs' condition is needed in order to ensure the existence of a value.…”

Value Function and Optimal Control of Differential Inclusions

“…This result is well known, when F (·) is locally Lipschitz [7,14,15,18]. We show that our assumptions are essentially weaker.…”

“…We refer to [15], where the value function is comprehensively studied for optimal control problems and for differential games.…”

Some Recent Aspects of Differential Game Theory

“…We also mention that some kind of constrained differential games with terminal cost can be treated by penalization method; this gives rise to differential games with discontinuous costs (cf. [103,108]). (5) are fulfilled.…”