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 constructive. 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.

Keywords: inverse optimal control, anthropomorphic control, transversality

@article{COCV_2013__19_4_1030_0, author = {Ajami, Alain and Gauthier, Jean-Paul and Maillot, Thibault and Serres, Ulysse}, title = {How humans fly}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1030--1054}, publisher = {EDP-Sciences}, volume = {19}, number = {4}, year = {2013}, doi = {10.1051/cocv/2012043}, mrnumber = {3182679}, zbl = {1280.93038}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2012043/} }

TY - JOUR AU - Ajami, Alain AU - Gauthier, Jean-Paul AU - Maillot, Thibault AU - Serres, Ulysse TI - How humans fly JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 1030 EP - 1054 VL - 19 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2012043/ DO - 10.1051/cocv/2012043 LA - en ID - COCV_2013__19_4_1030_0 ER -

%0 Journal Article %A Ajami, Alain %A Gauthier, Jean-Paul %A Maillot, Thibault %A Serres, Ulysse %T How humans fly %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 1030-1054 %V 19 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2012043/ %R 10.1051/cocv/2012043 %G en %F COCV_2013__19_4_1030_0

Ajami, Alain; Gauthier, Jean-Paul; Maillot, Thibault; Serres, Ulysse. How humans fly. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 4, pp. 1030-1054. doi : 10.1051/cocv/2012043. http://archive.numdam.org/articles/10.1051/cocv/2012043/

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