TY - GEN

T1 - Monotonicity of actuated flows on dissipative transport networks

AU - Zlotnik, Anatoly

AU - Misra, Sidhant

AU - Vuffray, Marc

AU - Chertkov, Michael

PY - 2017/1/6

Y1 - 2017/1/6

N2 - 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 The transferred commodity may be injected or withdrawn at any of the nodes, and is propelled throughout the network by nodally located compressors.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.

AB - 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 The transferred commodity may be injected or withdrawn at any of the nodes, and is propelled throughout the network by nodally located compressors.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.

UR - http://www.scopus.com/inward/record.url?scp=85015009552&partnerID=8YFLogxK

U2 - 10.1109/ECC.2016.7810392

DO - 10.1109/ECC.2016.7810392

M3 - Conference contribution

AN - SCOPUS:85015009552

T3 - 2016 European Control Conference, ECC 2016

SP - 831

EP - 836

BT - 2016 European Control Conference, ECC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 European Control Conference, ECC 2016

Y2 - 29 June 2016 through 1 July 2016

ER -