Continuity of the value function for exit time optimal control problems of hybrid systems

This paper proves the uniform continuity of the value function for exit time optimal control problems of hybrid systems with autonomous and controlled transitions. By extending conditions already used for purely continuous systems the paper provides the ground for numerical algorithms for dynamic programming of hybrid systems. Transversality conditions for the continuous dynamics at the guard set boundaries ensure that the continuity property of the value function is not altered by a discrete transition of the hybrid system.