Identification of LPV partial differential equation models

Abstract

This paper deals with the identification of linear parameter varying (LPV) models described by partial differential equations (PDE). A direct identification of continuous space-time LPV-EDP systems in an input-output setting is investigated in the case of an additive output noise. The continuous space-time LPV-PDE model is firstly proposed to be rewritten as a multi-input single-output linear time-space invariant model and an iterative optimization is then developed to estimate efficiently the model parameters. The performance of the proposed method is then illustrated via a representative simulation example based on an Alsace river-flow measurement.

Refined IV-based method for LPV partial differential equation model identification

“…In practice, the filters F (ð, θ) and the signalsχ (it,ix) are unknown and therefore an iterative procedure is proposed in order to cope with this issue, similarly as it is achieved in the approaches developed for the ODE case in [8] and [13] for the PDE case. However, the LS method delivers biased estimates in the general practical situation where the noise structure is not known.…”

“…This problem is well-known when dealing with LPV models. In [7] (for ODE models) and [13] (for PDE models), the proposed solution is to rewrite the LPV model as a MISO LTI model for which the PEM can be formulated. The idea here is to follow the same concept and to reformulate the LPV model in order to express it as a linear regression form:…”

“…The parameters are estimated by the proposed approach denoted as SRIVC and the LPV-SILS-PDE developed in [13] and denoted as SILS (for simplified iterative least squares). From both Tables, it can be noted that the estimates of the proposed SRIVC method are unbiased with relatively small standard deviations.…”

“…A method has been already proposed to identify a continuous space-time LPV partial differential equation model [13]. The approach is based on an iterative procedure develop to estimate efficiently the model parameters into the errorprediction minimization framework.…”