Freeway ramp metering based on robust integral of the sign of the error

Based on the characteristic of highly nonlinear and uncertain of traffic flow model for freeway, ramp metering was designed in the way of robust integral of the sign of the error (RISE). The unmodeled term in the model was estimated by its bounded differential. Because the control input was designed to achieve the estimated error closing to zero, the control effort is reduced. The controller is presented without approximately linearizing the macroscopic traffic flow model and knowing the upper bound of unmodeled term. The control approach is verified not only to be robust subject to uncertainties including external disturbances and unmodeled dynamics, but also to be adaptive to unknown parameters. A numerical example shows a satisfactory track performance.