Title: Analysis and Control of a Non-Standard Hyperbolic PDE Traffic Flow Model,
Abstract: The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear
traffic flow model on a bounded domain. The model consists of two first-order
PDEs with a dynamic boundary condition that involves the time derivative of the
velocity. The proposed model has features that are important from a
traffic-theoretic point of view: is completely anisotropic and information
travels forward exactly at the same speed as traffic. It is shown that, for all
physically meaningful initial conditions, the model admits a globally defined,
unique, classical solution that remains positive and bounded for all times.
Moreover, it is shown that global stabilization can be achieved for arbitrary
equilibria by means of an explicit boundary feedback law. The stabilizing
feedback law depends only on the inlet velocity and consequently, the
measurement requirements for the implementation of the proposed boundary
feedback law are minimal. The efficiency of the proposed boundary feedback law
is demonstrated by means of a numerical example.