Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • minimal time function
  • viscosity solutions
  • geodesic trajectories
  • proximal analysis
  • monotonicity of trajectories
  • nonsmooth analysis

Suggested citation

F. H. Clarke, C. Nour. “The Hamilton-Jacobi Equation of Minimal Time Control.” Journal of Convex Analysis 11 (2004), No. 2, 413–436.

Copyright Heldermann Verlag 2004