Parameter identifiability for nonlinear LPV models

Srinivasarengan, Krishnan ; Ragot, José ; Aubrun, Christophe ; Maquin, Didier

International Journal of Applied Mathematics and Computer Science, Tome 32 (2022) no. 2, pp. 255-269.

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.

Détail

Keywords: parameter identifiability, parameter estimation, linear parameter varying model, parity space approach, null space
Mots-clés : identyfikacja parametrów, szacowanie parametrów, spacja zerowa

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