Controllability of a fluid in a 1-D tank

Abstract

Listen

Translate article

We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. The motion of the fluid is assumed to be well-described by the Saint-Venant equations (also called the shallow water equations). We state a local controllability result for this nonlinear control system around every steady state. The main ingredients of the proof are sketched on toy models. We also recall on simple hyperbolic control systems some classical tools to prove the controllability in connection with time-delay control systems.