  We study dynamical transportation networks in a framework that includes
extensions of the classical Cell Transmission Model to arbitrary network
topologies. The dynamics are modeled as systems of ordinary differential
equations describing the traffic flow among a finite number of cells
interpreted as links of a directed network. Flows between contiguous cells, in
particular at junctions, are determined by merging and splitting rules within
constraints imposed by the cells' demand and supply functions as well as by the
drivers' turning preferences, while inflows at on-ramps are modeled as
exogenous and possibly time-varying.
  First, we analyze stability properties of dynamical transportation networks.
We associate to the dynamics a state-dependent dual graph whose connectivity
depends on the signs of the derivatives of the inter-cell flows with respect to
the densities. Sufficient conditions for the stability of equilibria and
periodic solutions are then provided in terms of the connectivity of such dual
graph.
  Then, we consider synthesis of control policies that use a combination of
turning preferences, speed limits, and ramp metering, in order to optimize
convex objectives. We first show that, in the general case, the optimal control
synthesis problem can be cast as a convex optimization problem, and that the
equilibrium of the controlled network is in free-flow. If the control policies
are restricted to speed limits and ramp metering, then the resulting synthesis
problem is still convex for networks where every node is either a merge or a
diverge junction, and where the dynamics is monotone. These results apply both
to the optimal selection of equilibria and periodic solutions, as well as to
finite-horizon network trajectory optimization.
  Finally, we illustrate our findings through simulations on a road network
inspired by the freeway system in southern Los Angeles.
