Stabilization of a 1-D tank modeled by the shallow water equations
Journées équations aux dérivées partielles (2002), article no. 13, 13 p.

We consider a tank containing a fluid. The tank is subjected to a one-dimensional 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.

Nous considérons un bac de fluide soumis à un déplacement longitudinal. Nous modélisons le mouvement du fluide par les équations de Saint-Venant dont les équations linéarisées ne sont pas stabilisables. A l'aide d'une approche Lyapunov, nous déduisons des lois de contrôles qui numériquement stabilisent l'état du fluide et du bac.

@article{JEDP_2002____A13_0,
     author = {Prieur, Christophe and de Halleux, Jonathan},
     title = {Stabilization of a 1-D tank modeled by the shallow water equations},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Universit\'e de Nantes},
     year = {2002},
     doi = {10.5802/jedp.611},
     mrnumber = {1968209},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2002____A13_0}
}
Prieur, Christophe; de Halleux, Jonathan. Stabilization of a 1-D tank modeled by the shallow water equations. Journées équations aux dérivées partielles (2002), article  no. 13, 13 p. doi : 10.5802/jedp.611. http://www.numdam.org/item/JEDP_2002____A13_0/

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