Mathematical Problems in Mechanics
Control of irrigation channels with variable bathymetry and time dependent stabilization rate
Comptes Rendus. Mathématique, Volume 346 (2008) no. 19-20, pp. 1119-1122.

This Note deals with the regulation of water flow in open-channels employing the shallow-water model with variable bathymetry. By using energy a priori estimation technics and the compactness theory, we build a stabilizing boundary control. The control law is based on an arbitrary choice of the time dependent stabilization rate r. Say, the energy decreases like the exponential of 0tr(s)ds when the time t tends to ∞.

Dans cette Note nous traitons un problème de contrôle des canaux d'irrigation à bathymétrie variable. En utilisant la technique d'estimation a priori de l'énergie et la théorie de la compacité, nous construisons un contrôle frontière. Ce dernier est basé sur le choix d'un taux de stabilisation r arbitraire et pouvant varier en fonction du temps. En effet, l'énergie décroît comme l'exponentielle de 0tr(s)ds quand le temps t tend vers ∞.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.09.009
Sene, Abdou 1; Wane, Bocar Amadou 2; Le Roux, Daniel Y. 2

1 UFR de sciences appliquées et technologie, Université Gaston-Berger, B.P. 234 Saint-Louis, Sénégal
2 Département de mathématiques et statistique, Université Laval, G1K 7P4 Québec, Québec, Canada
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Sene, Abdou; Wane, Bocar Amadou; Le Roux, Daniel Y. Control of irrigation channels with variable bathymetry and time dependent stabilization rate. Comptes Rendus. Mathématique, Volume 346 (2008) no. 19-20, pp. 1119-1122. doi : 10.1016/j.crma.2008.09.009. http://www.numdam.org/articles/10.1016/j.crma.2008.09.009/

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[2] Litrico, X. Robust flow control of single input multiple output regulated rivers, Journal of Irrigation and Drainage Engineering, Volume 127 (2001), pp. 281-286

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