Strong integral input-to-state stability in dynamical flow networks

G. Nilsson, S. Coogan
American Control Conference, 2021


Dynamical flow networks are vital in modeling many networks, such as transportation networks, distribution networks, and queuing networks. While the flow dynamics in such networks follow the conservation of mass on the links, the outflow from each link is often non-linear due to the actual flow dynamics, flow capacity constraints, and simultaneous service constraints. Such non-linear constraints imply a limit on the magnitude of exogenous inflows that a dynamical flow network can handle. This paper shows how the Strong integral Input-to-State Stability (Strong iISS) property allows for quantifying the effects of the exogenous inflow on the flow dynamics. The Strong iISS property enables a unified stability analysis of classes of dynamical flow networks that were only partly analyzable before, such as multi-commodity flow networks, networks with cycles, and networks with non-monotone flow dynamics. We first present sufficient conditions on the maximum magnitude of exogenous inflow to guarantee input-to-state stability for a dynamical flow network. We next exemplify the conditions by applying them to existing dynamical flow network models, specifically, fluid queuing models and multi-commodity flow models.