Hamilton-Jacobi inequalities on a metric space
Résumé
In some applied models (of flocking or of the crowd control) it is more natural to deal with elements of a metric space (as for instance a family of subsets of a vector space endowed with the Hausdorff metric) rather than with vectors in a normed vector space. We consider an optimal control problem on the so called morphological control system whose trajectories are time dependent tubes of subsets of R N and show that the theory of Hamilton-Jacobi-Bellman inequalities can be extended to this framework.
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