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Abstract: In this paper, we investigate a minimum time problem for controlled non-autonomous differential systems, with a dynamics depending on the final time. The minimal time function associated to this problem does not satisfy the dynamic programming principle. However, we will prove that it is related to a standard front propagation problem via the reachability function.
Mots Clés: Non-autonomous differential equations; Minimum time problem; Hamilton-Jacobi-Bellman equation; Reachability set; Target problem