Résumé
This paper(1) describes an original approach based on dynamic programming theory (discrete-time finite horizon Markov control) to address the difficult problem of computing optimal trajectories with respect to some criteria for any vehicle evolving in a given environment (in a probabilistic point of view) to accomplish some tasks (defined in a complex Lipschitz criteria). After a brief remind about dynamic programming The whole control process is detailled and applied in this paper for a submarine equipped with a sonar system which wants to detect targets as well as possible. Promising result about the optimal depth control for a submarine are presented with one and then two targets showing that the chosen approach is a good candidate.