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  • 标题:Stability and phase transitions of dynamical flow networks with finite capacities
  • 本地全文:下载
  • 作者:Leonardo Massai ; Giacomo Como ; Fabio Fagnani
  • 期刊名称:IFAC PapersOnLine
  • 印刷版ISSN:2405-8963
  • 出版年度:2020
  • 卷号:53
  • 期号:2
  • 页码:2588-2593
  • DOI:10.1016/j.ifacol.2020.12.306
  • 语种:English
  • 出版社:Elsevier
  • 摘要:AbstractWe study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell —consisting of the difference between the total flow directed towards it minus the outflow from it— exceeds a certain capacity constraint, then the exceeding part of it leaks out of the system. The ensuing network flow dynamics is a linear saturated system with compact state space that we analyse using tools from monotone systems and contraction theory. Specifically, we prove that there exists a set of equilibrium points that is globally asymptotically stable. Such set of equilibrium points reduces to a single globally asymptotically stable equilibrium point for generic exogenous demand vectors. Moreover, we show that the critical exogenous demand vectors giving rise to non-unique equilibrium points correspond to phase transitions in the asymptotic behavior of the dynamical flow network.
  • 关键词:KeywordsDynamical flow networksnonlinear systemscompartmental systemsnetwork flowsrobust control
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