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

Consider a rectangular tank containing an inviscid incompressible and irrotational 'uid. The tank is subject to a one-dimensional horizontal move (the control) and the motion of the 'uid is described by the shallow water equations. By means of a Lyapunov approach, control laws that stabilize the state of the 'uid–tank system are derived. Two classes of control are considered: full-state feedback and output feedback where the output is given by the trajectory of the tank, the level of the 'uid at the boundary of the tank and the time. Although global asymptotic stability is yet to be proved, stabilization is observed through numerical simulations. c © 2003 Elsevier B.V. All rights reserved.