Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
Université Paris-Sud, Département de Mathématique,
bâtiment 425, 91405 Orsay, France; Jean-Michel.Coron@math.u-psud.fr.
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.
Mathematics Subject Classification: 76B75 / 93B05 / 76B15 / 35F30
Key words: Controllability / hyperbolic systems / shallow water.
© EDP Sciences, SMAI, 2002