Observer design for a class of nonlinear systems

TLDR

The paper develops a viable design methodology to construct observers for a class of nonlinear systems. The proposed technique solves an offline Riccati equation to design observers for globally Lipschitz nonlinear systems, relaxes to local conditions for broader applicability, yields approximate observers for more general systems, and is illustrated on a single-link flexible joint robot to estimate link variables from joint measurements.

Abstract

A viable design methodology to construct observers for a class of nonlinear systems is developed. The proposed technique is based on the off-line solution of a Riccati equation, and can be solved using commercially available software packages. For globally valid results, the class of systems considered is characterized by globally Lipschitz nonlinearities. Local results relax this assumption to only a local requirement. For a more general description of nonlinear systems, the methodology yields approximate observers, locally. The proposed theory is used to design an observer for a single-link flexible joint robot. This observer estimates the robot link variables based on the joint measurements.