A DIFFERENTIAL GEOMETRIC VIEWPOINT ON LOCAL IDENTIFIABILITY AND IDENTIFICATION PART Ⅰ: THEORY

摘要

The questions of local identifiability and identification of nonlinear systems are treated from a differential geometric point of view. It is shown how identifiability can be interpreted in the framework of Lie groups, which provides convenient tools for a unifying concept of identifiability. Three different notions of identifiability are interpreted in this framework. Furthermore parameter identification itself is also treated. It is shown how a parameter estimator can be formulated in a coordinate-free setting. In this setting it can be clearly determined to what extent the underlying geometric structure and the coordinate-specific parameterization of the system influence the properties of the estimator.