TY - GEN

T1 - Linear programming based routing design for a class of positive systems with integral and capacity constraints

AU - Arneson, Heather

AU - Langbort, Cédric

N1 - Funding Information:
★ This work was funded in part by a NASA Illinois Space Grant Consortium seed grant and NSF grant #0826469 to C. Langbort, and NASA Illinois Space Grant Consortium Fellowship, University of Illinois College of Engineering SURGE Fellowship, and NASA Aeronautics Scholarship Program Fellowship to H. Arneson.

PY - 2009

Y1 - 2009

N2 - We present techniques to design routing parameters for positive compartmental conservative systems. Such systems capture the dynamics of some material owing through a network of interconnected reservoirs and have become popular, in particular, as models of air traffic fows. These techniques use Linear Programs (LP) to design static routing parameters for single destination networks with the following objectives: (a) minimize delay, (b) minimize delay and satisfy additional delay constraints which are formulated as integral constraints on the states of the network, and (c) satisfy capacity constraints. For each of these problems, we prove that the resulting closed loop systems are stable, positive, conservative and exhibit a user defined interconnection of sections. Additionally, problems (a) and (b) are shown to minimize delay over all choices of routing parameters such that the closed loop system exhibits these characteristics.

AB - We present techniques to design routing parameters for positive compartmental conservative systems. Such systems capture the dynamics of some material owing through a network of interconnected reservoirs and have become popular, in particular, as models of air traffic fows. These techniques use Linear Programs (LP) to design static routing parameters for single destination networks with the following objectives: (a) minimize delay, (b) minimize delay and satisfy additional delay constraints which are formulated as integral constraints on the states of the network, and (c) satisfy capacity constraints. For each of these problems, we prove that the resulting closed loop systems are stable, positive, conservative and exhibit a user defined interconnection of sections. Additionally, problems (a) and (b) are shown to minimize delay over all choices of routing parameters such that the closed loop system exhibits these characteristics.

KW - Air traffic ow management

KW - Capacity constraints

KW - Linear programming

KW - Network routing design

KW - Positive systems

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U2 - 10.3182/20090924-3-IT-4005.0092

DO - 10.3182/20090924-3-IT-4005.0092

M3 - Conference contribution

AN - SCOPUS:79960967868

SN - 9783902661524

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

SP - 352

EP - 357

BT - 1st IFAC Workshop on Estimation and Control of Networked Systems, NecSys'09

T2 - 1st IFAC Workshop on Estimation and Control of Networked Systems, NecSys'09

Y2 - 24 September 2009 through 26 September 2009

ER -