Nonlinear parameter-varying embeddings for nonlinear state estimation with application to a two-link robot manipulator

Abstract

Observer design for nonlinear systems is a relevant and challenging task in systems and control design. In this work, we follow the idea of embedding the system in the class of nonlinear parameter-varying systems to benefit from linear structures as in a standard LPV embedding while keeping some nonlinear structures and, thus, reducing the numbers of scheduling-parameters in the representation. We lay out the NLPV observer design procedure for general nonlinear systems, propose a number of improvements, and exemplify the application for a two-arm robot model. In a numerical study, we compare the performance of the NLPV design to established standard nonlinear approaches such as the \emph{extended Kalman filter} and the \emph{moving horizon estimation}.