Stabilization of a 1-D tank modeled by the shallow water equations

We consider a tank containing a fluid. The tank is subjected to a onedimensional horizontal move and the motion of the fluid is described by the shallow water equations. By means of a Lyapunov approach, we deduce control laws to stabilize the fluid’s state and the tank’s position. Although global asymptotic stability is yet to be proved, we numerically simulate the system and observe the stabilization for different control situations.