State observation for heterogeneous quasilinear traffic flow system with disturbances

This paper studies state observation for a heterogeneous quasilinear traffic flow system with disturbances at the inlet of a considered road section. Based on the backstepping method, an observer is designed for the quasilinear traffic flow system with only the boundary measurements at the inlet of the considered road section. The observer is constructed by duplicating the quasilinear system and adding the output injection terms to the partial differential equations and boundary conditions. Making use of the backstepping transformation, the injection gains of the observer system are derived by the computation of kernel equations, which are obtained by mapping the error system into an integral input-to-state stable target system. The applicability of the observer for the design of an output feedback controller stabilizing the quasilinear system is discussed. Finally the assumptions of the design of the observer are numerically checked on a realistic congested traffic scenario.