A feedback linearization approach for closed-loop control design: Application to variable speed limits and ramp metering

The growing level of freeway traffic congestion comprises an everyday life issue with social, economic, and environmental implications for modern metropolitan areas. Although there is evidence that Variable Speed Limits (VSL) and Ramp Metering (RM) are two effective practical approaches to ameliorate traffic congestion, their real-time field application is deemed cumbersome due to computational complexities. The positive effects that these approaches can have on traffic flow and congestion can be demonstrated with the augmented METANET model, which is one of the most widely used macroscopic models for freeway traffic. From the mathematical and systems theory viewpoint, METANET is a nonlinear, non-affine, Multiple Input Multiple Output (MIMO) system, which is affected by disturbances. Feedback linearization is a useful methodology in the literature to deal with nonlinear MIMO systems, and simplify the control design procedure. In the current work, by applying this method, we manage to represent the closed-loop system with a linear model that under certain conditions be an exact replication of the original system. Furthermore, the existence of a zero dynamic system, the controller stability, and the disturbance decoupling problem are investigated. Afterwards, we present and discuss the closed-loop linear representation of the METANET model by applying an appropriate feedback linearization method. Finally, a pole placement feedback loop is developed to regulate the closed-loop linear model