  Motivated by the fact that intelligent traffic control systems have become
inevitable demand to cope with the risk of traffic congestion in urban areas,
this paper develops a distributed control strategy for urban traffic networks.
Since these networks contain a large number of roads having different
directions, each of them can be described as a multi-agent system. Thus, a
coordination among traffic flows is required to optimize the operation of the
overall network. In order to determine control decisions, we describe the
objective of improving traffic conditions as a constrained optimization problem
with respect to downstream traffic flows. By applying the gradient projection
method and the minimal polynomial of a matrix pair, we propose algorithms that
allow each road cell to determine its control decision corresponding to the
optimal solution while using only its local information. The effectiveness of
our proposed algorithms is validated by numerical simulations.
