Exact and positive controllability of boundary control systems

Klaus-Jochen Engel; Marjeta Kramar FijavŽ; Klaus-Jochen Engel; Marjeta Kramar FijavŽ

doi:10.3934/nhm.2017014

Networks and Heterogeneous Media

2017, Volume 12, Issue 2: 319-337. doi: 10.3934/nhm.2017014

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Exact and positive controllability of boundary control systems

Klaus-Jochen Engel ^{1
,},
Marjeta Kramar FijavŽ ^{2,3
,
,}

1.
University of L'Aquila, Department of Information Engineering, Computer Science and Mathematics, Via Vetoio, Coppito, I-67100 L'Aquila (AQ), Italy
2.
University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana, Slovenia
3.
Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia

Received: 01 September 2016 Revised: 01 January 2017
Primary: 93B05; Secondary: 47N70, 35R02

We characterize the space of all exactly reachable states of an abstract boundary control system using a semigroup approach. Moreover, we study the case when the controls of the system are constrained to be positive. The abstract results are then applied to study flows in networks with static as well as dynamic boundary conditions.
- Boundary control,
- positive control,
- operator semigroups,
- reachability spaces,
- Kalman condition,
- flows in networks
Citation: Klaus-Jochen Engel, Marjeta Kramar FijavŽ. Exact and positive controllability of boundary control systems[J]. Networks and Heterogeneous Media, 2017, 12(2): 319-337. doi: 10.3934/nhm.2017014

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Abstract

We characterize the space of all exactly reachable states of an abstract boundary control system using a semigroup approach. Moreover, we study the case when the controls of the system are constrained to be positive. The abstract results are then applied to study flows in networks with static as well as dynamic boundary conditions.

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