Mathematics

This talk 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 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.This starting point is the reason for the particular classes of control systems and of costs under consideration.To summarize, our conclusion is that genericaly, inside these classes, three experiments visiting the same values of the control are needed to reconstruct the cost function, and two experiments are in general not enough. The method is constructive and the proof of the results is mostly based upon Thom's transversality theory.