Collocated Observer Design Based on Continuum Backstepping for a Class of Hyperbolic PDEs

A collocated observer design approach is addressed, which is based on the continuum backstepping algorithm for partial differential equations (PDEs) with boundary feedback. This observer for a class of hyperbolic PDEs is constructed through an integral form with undetermined kernel functions, combining with the “inverse” Volterra transformation and using the position and velocity of the collocated end as feedback through the boundary input with the Neumann type. The error system is transformed into the exponentially stable transformed system in the mapping space. The exponential stability of the source system is achieved with norm restrictions between the original and the transformed systems.