Distributed consensus-based switched observers for freeway traffic density estimation

The estimation of traffic densities in portions of road links is an important open problem. This work contributes to the topic proposing a distributed switched observer design method, based on Luenberger-like and consensus ideas. To this aim, a switching mode model (SMM) is employed, representing the freeway system switching among different sets of linear difference equations. The proposed scheme allows every observer to estimate the densities of the overall system, with very limited information exchange requirements between observers. Asymptotic stability of the overall scheme is proved when the system operates under observable modes, together with L2-gain disturbance rejection capabilities. The solution is provided in terms of a set of LMIs that use the structure of the SMM to alleviate the computational requirements. The effectiveness of the approach is shown with simulation examples.