On the hyperbolic observer canonical form

Abstract:
Observer design for a class of distributed parameter systems based on the so called hyperbolic observer canonical form (o.c.f.) is considered. The method relies on the tight relation between hyperbolic d.p.s. and functional differential equations (f.d.e.). Based on an input-output description given in form of a f.d.e. and a parametrization of the original “physical” coordinates by the system’s input and output trajectories, the transformation to the o.c.f. is calculated using another set of coordinates. These coordinates are associated with the hyperbolic observability form and correspond to the restriction of the output trajectory to a certain interval. The proposed method is illustrated on the basis of the one-dimensional wave equation with dynamic boundary conditions.