An extended instrument variable approach for nonparametric LPV model identification

Abstract

Linear parameter varying models (LPV) have proven to be effective to describe non–linearities and time–varying behaviors. In this work, a new non-parametric estimation algorithm for state-space LPV models based on support vector machines is presented. This technique allows the functional dependence between the model coefficients and the scheduling signal to be “learned” from the input and output data. The proposed algorithm is formulated in the context of instrumental (IV) estimators, in order to obtain consistent estimates for general noise conditions. The method is based on a canonical state–space representation and admits a predictor form that has shown to be suitable for system identification, as it leads to a convenient regression form. In addition, this predictor has an inherent filtering feature. In the context of vector support machines, such filtering mechanism leads to two–dimensional data processing, which can be used to decrease the variance of estimates due to noisy data. The performance of the proposed approach is evaluated from simulated data subject to different noise scenarios. The technique was able to reduce the error due to the variance of the estimator in most of the analyzed scenarios. © 2018