Controllability and stabilization of a moving water tank system considering fluid-structure interaction

This paper deals with the modeling and the mathematical analysis of problems involving a rectangular container installed on a cart. The overall system is controlled via a longitudinal force in order to move the cart from one location to another, and the key problem is the suppression of sloshing during transportation. We firstly make a precise mathematical analysis of the model in order to obtain a system under an adequate form, in order to study some controllability and stabilization problems with standard techniques. Note that in this paper, we want to control and stabilize simultaneously the fluid and the cart. We show that the system is not approximately controllable in finite time, but only on [0, infin). We also study the stabilization of the system with two different static feedbacks. The first feedback uses the observation of the cart speed only. The second feedback uses the cart speed and a measurement of the elevation of the free surface of the fluid in the container. We show that strong stability holds in both cases, although the coupled system is not dissipative for the second type of feedback