Robust tracking control design for fluid traffic dynamics

The paper is devoted to the boundary control of the traffic system described by the LWR model with a triangular fundamental diagram and a space-dependent in-domain unknown disturbance, which can be described as an inhomogeneous transport equation. The controller design strategy aims first at stabilizing the deviation from the desired time-dependent trajectory and then at minimizing the deviation in the sense of two possible space-norms (i.e. L
₂
and L
_∞
). Numerical simulations for both L
₂
and L
_∞
minimization cases obtained with this are presented to evaluate the improvements control design.