State estimation for nonlinear hyperbolic PDE-ODE cascade systems

This paper presents state estimation for a class of nonlinear hyperbolic PDE-ODE cascade systems. The observer is based on the backstepping method and relies only on a single boundary measurement. The observer consists of a copy of the plant plus output injection terms both in the PDEs and the ODEs. Furthermore, both sensing and actuation are located at the same boundary (collocated setup). The observer gains are computed analytically by solving Goursat-type PDEs in terms of modified Bessel functions of the first kind. A field-scale test experiment in a flow-loop test facilities is conducted by Statoil oil company to show the applicability of the observer.