This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration.
Mots-clés : optimal control, inversion, adjoint states, normal form
@article{COCV_2008__14_2_294_0,
author = {Petit, Nicolas and Chaplais, Fran\c{c}ois},
title = {Inversion in indirect optimal control of multivariable systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {294--317},
publisher = {EDP-Sciences},
volume = {14},
number = {2},
year = {2008},
doi = {10.1051/cocv:2007054},
mrnumber = {2394512},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2007054/}
}
TY - JOUR AU - Petit, Nicolas AU - Chaplais, François TI - Inversion in indirect optimal control of multivariable systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 294 EP - 317 VL - 14 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2007054/ DO - 10.1051/cocv:2007054 LA - en ID - COCV_2008__14_2_294_0 ER -
%0 Journal Article %A Petit, Nicolas %A Chaplais, François %T Inversion in indirect optimal control of multivariable systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 294-317 %V 14 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2007054/ %R 10.1051/cocv:2007054 %G en %F COCV_2008__14_2_294_0
Petit, Nicolas; Chaplais, François. Inversion in indirect optimal control of multivariable systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 294-317. doi : 10.1051/cocv:2007054. http://archive.numdam.org/articles/10.1051/cocv:2007054/
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