Stability of dynamical distribution networks with arbitrary flow constraints and unknown in/outflows

A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and outflows. We analyze the dynamics of the system in closed-loop with a distributed proportional-integral controller structure, where the flow inputs are constrained to take value in closed intervals. Results from our previous work are extended to general flow constraint intervals, and conditions for asymptotic load balancing are derived that rely on the structure of the graph and its flow constraints.

[1]  Frank Allgöwer,et al.  Network clustering: A dynamical systems and saddle-point perspective , 2011, IEEE Conference on Decision and Control and European Control Conference.

[2]  Franco Blanchini,et al.  Control of production-distribution systems with unknown inputs and system failures , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[3]  Frank Harary,et al.  Graph Theory , 2016 .

[4]  Arjan van der Schaft,et al.  Load balancing of dynamical distribution networks with flow constraints and unknown in/outflows , 2013, Syst. Control. Lett..

[5]  Claudio De Persis,et al.  Balancing time-varying demand-supply in distribution networks: An internal model approach , 2013, 2013 European Control Conference (ECC).

[6]  Bernhard Maschke,et al.  Port-Hamiltonian Dynamics on Graphs: Consensus and Coordination Control Algorithms , 2010 .

[7]  Arjan van der Schaft,et al.  Port-Hamiltonian Systems on Graphs , 2011, SIAM J. Control. Optim..

[8]  Mehran Mesbahi,et al.  Edge Agreement: Graph-Theoretic Performance Bounds and Passivity Analysis , 2011, IEEE Transactions on Automatic Control.

[9]  Franco Blanchini,et al.  A decentralized solution for the constrained minimum cost flow , 2010, 49th IEEE Conference on Decision and Control (CDC).

[10]  Arjan van der Schaft,et al.  A Hamiltonian perspective on the control of dynamical distribution networks , 2012 .

[11]  A. Schaft,et al.  The Hamiltonian formulation of energy conserving physical systems with external ports , 1995 .