Monotonicity of actuated flows on dissipative transport networks

Anatoly Zlotnik, Sidhant Misra, Marc Vuffray, Michael Chertkov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations


We derive a monotonicity property for general, transient flows of a commodity transferred throughout a network, where the flow is characterized by density and mass flux dynamics on the edges with density continuity and mass balance conditions at the nodes. The dynamics on each edge are represented by a general system of partial differential equations that approximates subsonic compressible fluid flow with energy dissipation. The transferred commodity may be injected or withdrawn at any of the nodes, and is propelled throughout the network by nodally located compressors. These compressors are controllable actuators that provide a means to manipulate flows through the network, which we therefore consider as a control system. A canonical problem requires compressor control protocols to be chosen such that time-varying nodal commodity withdrawal profiles are delivered and the density remains within strict limits while an economic or operational cost objective is optimized. In this manuscript, we consider the situation where each nodal commodity withdrawal profile is uncertain, but is bounded within known maximum and minimum time-dependent limits. We introduce the monotone parameterized control system property, and prove that general dynamic dissipative network flows possess this characteristic under certain conditions. This property facilitates very efficient formulation of optimal control problems for such systems in which the solutions must be robust with respect to commodity withdrawal uncertainty. We discuss several applications in which such control problems arise and where monotonicity enables simplified characterization of system behavior.

Original languageEnglish (US)
Title of host publication2016 European Control Conference, ECC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781509025916
StatePublished - 2016
Externally publishedYes
Event2016 European Control Conference, ECC 2016 - Aalborg, Denmark
Duration: Jun 29 2016Jul 1 2016

Publication series

Name2016 European Control Conference, ECC 2016


Conference2016 European Control Conference, ECC 2016

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization


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