15 research outputs found
Conjugate times and regularity of the minimum time function with differential inclusions
This paper studies the regularity of the minimum time function, ,
for a control system with a general closed target, taking the state equation in
the form of a differential inclusion. Our first result is a sensitivity
relation which guarantees the propagation of the proximal subdifferential of
along any optimal trajectory. Then, we obtain the local regularity of
the minimum time function along optimal trajectories by using such a relation
to exclude the presence of conjugate times
On differential games with long-time-average cost
The paper deals with the ergodicity of deterministic zero-sum differential games with long-time-average cost. Some new sufficient conditions are given, as well as a class of games that are not ergodic. In particular, we settle the issue of ergodicity for the simple games whose associated Isaacs equation is a convex-concave eikonal equation