Vertex control of flows in networks

Klaus-Jochen Engel; Marjeta Kramar Fijavž; Rainer Nagel; Eszter Sikolya

doi:10.3934/nhm.2008.3.709

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2008, Volume 3, Issue 4: 709-722. Doi: 10.3934/nhm.2008.3.709

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Vertex control of flows in networks

1.
University of L'Aquila, Faculty of Engineering, Piazzale E. Pontieri 2, I-67100 Monteluco di Roio (L’Aquila)
2.
University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana
3.
University of Tübingen, Mathematics Institute, Auf der Morgenstelle 10, D-72076 Tübingen
4.
Eötvös Loránd University Budapest, Department of Applied Analysis, Pázmány Péter sétány 1/c., Budapest H-1117

Received: March 31, 2008

Revised: May 31, 2008

Published: November 2008

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Abstract

We study a transport equation in a network and control it in a single vertex. We describe all possible reachable states and prove a criterion of Kalman type for those vertices in which the problem is maximally controllable. The results are then applied to concrete networks to show the complexity of the problem.

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Mathematics Subject Classification: 34B45, 93B05, 47N70.

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