LOCAL CONTROLLABILITY OF A 1-D TANK CONTAINING A FLUID MODELED BY THE SHALLOW WATER EQUATIONS

@inproceedings{Coron2002LOCALCO,
  title={LOCAL CONTROLLABILITY OF A 1-D TANK CONTAINING A FLUID MODELED BY THE SHALLOW WATER EQUATIONS},
  author={Jean-Michel Coron},
  year={2002}
}
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. 

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