Backstepping Design of Dynamic Observers for Hyperbolic Systems

Abstract

This letter considers the backstepping design of dynamically extended observers, or dynamic observers for short, for systems described by heterodirectional hyperbolic partial differential equations based on a collocated boundary measurement. In contrast to classical Luenberger-type observers, which usually consist of a copy of the system dynamics with appropriate injections of the measurement error, the dynamic observer incorporates an additional dynamics. The latter is chosen so that the extended observer error dynamics admits homogenized transport velocities on the unit spatial interval. With the added flexibility of the dynamic observer, using backstepping, it is possible to obtain a desired stable extended observer error dynamics with arbitrary in-domain couplings. An example illustrates the new dynamic observer design.