This paper is devoted to the general problem of reconstructing the cost from the
observation of trajectories, in a problem of optimal control. It is motivated by the
following applied problem, concerning HALE drones: one would like them to decide by
themselves for their trajectories, and to behave at least as a good human pilot. This
applied question is very similar to the problem of determining what is minimized in human
locomotion. These starting points are the reasons for the particular classes of control
systems and of costs under consideration. To summarize, our conclusion is that in general,
inside these classes, three experiments visiting the same values of the control are needed
to reconstruct the cost, and two experiments are in general not enough. The method is
The proof of these results is mostly based upon the Thom’s transversality theory.
This study is partly supported by FUI AAP9 project SHARE, and by ANR Project GCM, program
“blanche”, project number NT09-504490.