Control of irrigation channels with variable bathymetry and time dependent stabilization rate

Abdou Sene; Bocar Amadou Wane; Daniel Y. Le Roux

doi:10.1016/j.crma.2008.09.009

Mathematical Problems in Mechanics

Control of irrigation channels with variable bathymetry and time dependent stabilization rate

Presented by: Philippe G. Ciarlet

Abdou Sene ¹; Bocar Amadou Wane ²; Daniel Y. Le Roux 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

Comptes Rendus. Mathématique, Volume 346 (2008) no. 19-20, pp. 1119-1122.

Abstract (Original language)
Résumé

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 $- \int_{0}^{t} r (s) d s$ 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 $- \int_{0}^{t} r (s) d s$ quand le temps t tend vers ∞.

Received: 2007-10-18
Accepted: 2008-09-04
Published online: 2008-09-27

DOI: 10.1016/j.crma.2008.09.009

Author's affiliations:

Abdou Sene ¹; Bocar Amadou Wane ²; Daniel Y. Le Roux 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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     author = {Abdou Sene and Bocar Amadou Wane and Daniel Y. Le Roux},
     title = {Control of irrigation channels with variable bathymetry and time dependent stabilization rate},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1119--1122},
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     number = {19-20},
     year = {2008},
     doi = {10.1016/j.crma.2008.09.009},
     language = {en},
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Abdou Sene; Bocar Amadou Wane; Daniel Y. Le Roux. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.09.009/

References
Cited by

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

[3] P. Malaterre Pilot: linear quadratic optimal controller for irrigation canals, Journal of Irrigation and Drainage Engineering, Volume 124 (1998), pp. 187-194

[4] M. Ndiaye; G. Bastin Commande frontière adaptative d'un bief de canal avec prélèvements inconnus, RS-JESA, Volume 38 (2004), pp. 347-371

[5] C.Z. Xu, G. Sallet, Proportional and integral regulation of irrigation canal systems governed by the Saint-Venant equation, in: 14th IFAC World Congress, Beijing, China, 1999

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