Parameter identifiability for nonlinear LPV models
Résumé
Linear parameter varying (LPV) models are being increasingly used as a bridge between linear and nonlinear models.
From a mathematical point of view, a large class of nonlinear models can be rewritten in LPV or quasi-LPV forms easing
their analysis. From a practical point of view, that kind of model can be used for introducing varying model parameters
representing, for example, nonconstant characteristics of a component or an equipment degradation. This approach is
frequently employed in several model-based system maintenance methods. The identifiability of these parameters is then
a key issue for estimating their values based on which a decision can be made. However, the problem of identifiability
of these models is still at a nascent stage. In this paper, we propose an approach to verify the identifiability of unknown
parameters for LPV or quasi-LPV state-space models. It makes use of a parity-space like formulation to eliminate the states
of the model. The resulting input-output-parameter equation is analyzed to verify the identifiability of the original model or
a subset of unknown parameters. This approach provides a framework for both continuous-time and discrete-time models
and is illustrated through various examples.