American Institute of Mathematical Sciences

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December  2008, 3(4): 709-722. doi: 10.3934/nhm.2008.3.709

Vertex control of flows in networks

Klaus-Jochen Engel 1, , Marjeta Kramar Fijavž 2, , Rainer Nagel 3, and  Eszter Sikolya 4,

1. 

University of L'Aquila, Faculty of Engineering, Piazzale E. Pontieri 2, I-67100 Monteluco di Roio (L’Aquila), Italy
2. 

University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana, Slovenia
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, Hungary

Received  April 2008 Revised  June 2008 Published  October 2008

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.
Keywords: operator semigroups, boundary control, transport equation, networks.
Mathematics Subject Classification: 34B45, 93B05, 47N70.
Citation: Klaus-Jochen Engel, Marjeta Kramar Fijavž, Rainer Nagel, Eszter Sikolya. Vertex control of flows in networks. Networks & Heterogeneous Media, 2008, 3 (4) : 709-722. doi: 10.3934/nhm.2008.3.709
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