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We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint-Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.
@article{COCV_2002__8__513_0,
author = {Coron, Jean-Michel},
title = {Local controllability of a {1-D} tank containing a fluid modeled by the shallow water equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {513--554},
publisher = {EDP-Sciences},
volume = {8},
year = {2002},
doi = {10.1051/cocv:2002050},
mrnumber = {1932962},
zbl = {1071.76012},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002050/}
}
TY - JOUR AU - Coron, Jean-Michel TI - Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 513 EP - 554 VL - 8 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002050/ DO - 10.1051/cocv:2002050 LA - en ID - COCV_2002__8__513_0 ER -
%0 Journal Article %A Coron, Jean-Michel %T Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 513-554 %V 8 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002050/ %R 10.1051/cocv:2002050 %G en %F COCV_2002__8__513_0
Coron, Jean-Michel. Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 513-554. doi: 10.1051/cocv:2002050
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