Zero-sum state constrained differential games: existence of value for Bolza problem

• DOI: 10.1007/s00182-006-0030-9
• Publication Date: 2006-09-09T19:53:59Z
• Authors: Piernicola Bettiol; Pierre Cardaliaguet; Marc Quincampoix
• Keywords: Differential game; Value (mathematics); Zero (linguistics); Viscosity solution; Differential inclusion

We prove the existence of a lower semicontinuous value function for Bolza problem in differential games with state-constraints. As a byproduct, we obtain a new estimation of trajectories of a control system by trajectories with state constraints. This result which could be interesting by itself enables us to build a suitable strategy for constrained differential games. We also characterize the value function by means of viscosity solutions and give conditions under which the value function is locally Lipschitz continuous.