Nichtlineare stetige Beobachter

Abstract

AbstractMost state estimation methods for smooth nonlinear systems are also smooth and require that the Taylor linearization of the system is observable. The presented design of continuous observers can be applied if the nonlinear system is observable but not its Taylor linearization. In this case, the observability map of the system is a semi‐diffeomorphism which means that the map has only a continuous (and no smooth) inverse. A continuous observer is designed in the observability normal form coordinates and comprises a dynamic and an algebraic part. At least the algebraic part defined by the inverse observability map is continuous.The continuous observer approach can also be used to solve the critical observation problem if the Taylor linearization has only non‐detectable eigenvalues with a zero real part. Moreover, this approach allows an extension of the nonlinear normal form observer design because the observability rank condition is no more required. As distinct from the first presentation of continuous observers an [9], the design of nonlinear continuous observers is treated from a more applied point of view and is illustrated by examples for which smooth observers do not exist.