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Journal of Convex Analysis 11 (2004), No. 2, 413--436
Copyright Heldermann Verlag 2004

The Hamilton-Jacobi Equation of Minimal Time Control


F. H. Clarke
Institut Girard Desargues, Universite Lyon I, 21 Av. Claude Bernard, 69622 Villeurbanne, France, clarke@igd.univ.lyon1.fr

C. Nour
Institut Girard Desargues, Universite Lyon I, 21 Av. Claude Bernard, 69622 Villeurbanne, France, chadi@igd.univ.lyon1.fr

We study the solutions of the Hamilton-Jacobi equation that arise in connection with minimal time control, in a new global framework. These solutions, for which we establish existence using the minimal time function as a function of two variables, turn out to be closely related to time-geodesic trajectories.

Keywords: minimal time function, viscosity solutions, geodesic trajectories, proximal analysis, monotonicity of trajectories, nonsmooth analysis.

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