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Local controllability of a 1-D tank containing a fluid modeledby the shallow water equations

Published online by Cambridge University Press:  15 August 2002

Jean-Michel Coron
Jean-Michel Coron*
Affiliation:
Université Paris-Sud, Département de Mathématique, bâtiment 425, 91405 Orsay, France; Jean-Michel.Coron@math.u-psud.fr.
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Abstract

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.

Keywords

Controllabilityhyperbolic systemsshallow water.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 513 - 554
Copyright
© EDP Sciences, SMAI, 2002

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