15 research outputs found

    Conjugate times and regularity of the minimum time function with differential inclusions

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    This paper studies the regularity of the minimum time function, T(â‹…)T(\cdot), 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 TT along any optimal trajectory. Then, we obtain the local C2C^2 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

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    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
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