Vertex control of flows in networks

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

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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

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.
- networks,
- boundary control,
- transport equation,
- operator semigroups
Citation: Klaus-Jochen Engel, Marjeta Kramar Fijavž, Rainer Nagel, Eszter Sikolya. Vertex control of flows in networks[J]. Networks and Heterogeneous Media, 2008, 3(4): 709-722. doi: 10.3934/nhm.2008.3.709

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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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