@article{e28bb3bb7237454aa3c505f2ee052149,
title = "Optimal control of a water distribution network by two multilevel methods",
abstract = "The problem of daily controlling a water distribution network, including pumping devices and storage capacities, in order to supply the consumers at the lowest cost is formulated as a constrained optimal control problem. Discrete Dynamic Programming seems the only way to overcome the particular difficulties of this problem but the dimensionality prevents one using it on the global problem. Two approaches are considered. The first one consists in tearing up the network into several subnetworks and to use an algorithm of coordination. It succeeds in case of weak coupling between subnetworks. The second one uses an original approach of aggregation and disaggregation iteratively. Presently available experiments with the latter method showed its satisfactory behaviour.",
keywords = "Aggregation, computer control, coordination, dynamic programming, hierarchical systems, large-scale systems, optimal control, water resources",
author = "G{\'e}rald Joalland and Guy Cohen",
note = "Funding Information: THE WATER distribution network of interest belongs to the Soci6t6 Lyonnaise des Eaux et de l'Eclairage (SLEE), one of the main French companies in water distribution. It covers a large area in the Southern region of Paris, including 94 municipalities with 770 000 inhabitants and many industrialial consumers. It has distributed 71 million m 3 in 1975, through 2,871 km of pipes with diameters ranging from 0.003 to 1.200m. The greatest part of the network is interconnected and includes 7 main tanks, 3 production points on the river Seine, and 12 others producing underground water. Each production point is equipped with several on off pumps (consuming electric power) which can work either separately or simultaneously, with a range of possible combinations. Moreover, 18 boosters allow the supply of outlying districts. The river separates the network into two parts which were independent in the past but which now are connected and will become more connected in the future. In the same way, many small and isolated networks, which were easy to control, have been connected together, for the sake of reliability and other economic considerations, resulting in the present intricate situation. Therefore, the control which is still achieved by human operators has a tendency to become more and more centralized, while simultaneously becoming difficult without help from a computer. In 1975, SLEE decided to start a research project with the financial support of the D616gation G6n6rale ~ la Recherche Scientifique et Technique (DGRST). Our research team has been in charge of designing a mathematical method yielding a *Received December 11, 1978; revised July 9, 1978. The original version of this paper was presented at the 7th IFAC Congress on A Link Between Science and Applications of Automatic Control which was held in Helsinki, Finland during June 1978. The published Proceedings of this IFAC Meeting may be ordered from: Pergamon Press Limited, Headington Hill Hall, Oxford, OX30BW, U.K. This paper was recommended for publication in revised form by associate editor Y. Bar-Shalom This research has been supported by the D616gation G6n6rale /l la Recherche Scientifique et Technique, DGRST-France, under contract no. 75.7.1523. tPresently with the Operations Research Group of Cr6dit Lyonnais, Paris, on leave from Centre d'Automatique et Informatique, ENSMP, Fontainebleau, France. ++Centre d'Automatique et lnformatique, ENSMP, Fontainebleau, and IRIA-Laboria, Le Chesnay, France.",
year = "1980",
month = jan,
day = "1",
doi = "10.1016/0005-1098(80)90089-8",
language = "English",
volume = "16",
pages = "83--88",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier Ltd.",
number = "1",
}