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Abstract : We consider a target problem for a nonlinear system under state constraints. We give a new continuous level-set approach for characterizing the optimal times and the backward-reachability sets. This approach leads to a characterization via a Hamilton-Jacobi equation, without assuming any controllability assumption. We also treat the case of time-dependant state constraints, as well as a target problem for a two-player game with state constraints. Our method gives a good framework for numerical approximations,and some numerical illustrations are included in the paper.
Mots Clés: Minimal time problem; Hamilton-Jacobi-Bellman equations; Level set method; Reachability set (Attainable set); State constraints; Two-player game