Smooth Switching H∞ PI Controller for Local Traffic On-ramp Metering, an LMI Approach

This paper deals with the design of a bank of robust H∞ PI controllers for local traffic control. Traffic flow is modeled by the Uncertain Cell Transmission Model (UCTM) which is an affine switched model. It switches between different operating modes according to the traffic state (state dependent switching) and the uncertain parameters of the system. A robust PI controller is calculated for each mode of the UCTM. Since the switching law contains uncertainties we use a convex combination of controllers when the operating mode is uncertain. This smooth switching rule is motivated by statistical analysis of field data. The global stability of the closed loop system is proven by computing a PieceWise Quadratic (PWQ) Lyapunov function. A LMI is given to calculate the controllers. The approach is illustrated and validated in a study-case simulation.