  We study transportation networks controlled by dynamical feedback tolls. We
consider a multiscale transportation network model whereby the dynamics of the
traffic flows are intertwined with those of the drivers' route choices. The
latter are influenced by the congestion status on the whole network as well as
dynamic tolls set by the system operator. Our main result shows that a broad
class of decentralized congestion-dependent tolls globally stabilise the
transportation network around a Wardrop equilibrium. Moreover, using dynamic
marginal cost tolls, stability of the transportation network can be guaranteed
around the social optimum traffic assignment. This is particularly remarkable
as the considered decentralized feedback toll policies do not require any
global information about the network structure or the exogenous traffic load on
the network or state and can be computed in a fully local way. We also evaluate
the performance of these feedback toll policies both in the asymptotic and
during the transient regime, through numerical simulations.
