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

Jean-Michel Coron

ESAIM: Control, Optimisation and Calculus of Variations (2002)

  • Volume: 8, page 513-554
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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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 8 (2002): 513-554. <http://eudml.org/doc/244897>.

@article{Coron2002,
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.},
author = {Coron, Jean-Michel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {controllability; hyperbolic systems; shallow water; Saint-Venant equations},
language = {eng},
pages = {513-554},
publisher = {EDP-Sciences},
title = {Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations},
url = {http://eudml.org/doc/244897},
volume = {8},
year = {2002},
}

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
PB - EDP-Sciences
VL - 8
SP - 513
EP - 554
AB - 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.
LA - eng
KW - controllability; hyperbolic systems; shallow water; Saint-Venant equations
UR - http://eudml.org/doc/244897
ER -

References

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Citations in EuDML Documents

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  1. Lionel Rosier, Control of the surface of a fluid by a wavemaker
  2. Lionel Rosier, Control of the surface of a fluid by a wavemaker
  3. Olivier Glass, A controllability result for the 1 -D isentropic Euler equation
  4. Karine Beauchard, Controllability of Schrödinger equations
  5. Eduardo Cerpa, Emmanuelle Crépeau, Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain
  6. Karine Beauchard, Controllability of a quantum particle in a 1D variable domain
  7. Thierry Horsin, Local exact lagrangian controllability of the Burgers viscous equation
  8. Karine Beauchard, Controllablity of a quantum particle in a 1D variable domain

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