Abstract

The search for efficient algorithms and methods for multivariable LPV system identification has advanced mainly for the case of deterministic identification, partially due to the complexity increase tendency for modeling systems from LPV data for the stochastic case. In this work, methods, and algorithms for state space identification of multivariable LPV stochastic systems based on extensions of the minimal stochastic realization theory of Akaike are proposed. For the methods ICCALPV and 3C2ILPV here proposed, we extend the conditional canonical correlation identification method for LTI systems of Katayama/Larimore to stochastic LPV systems and use successive approximations to obtain the LPV model with affine parameter dependence. For the K2SIDLPV and 3CKLPV methods, also here proposed, the kernelizations of the canonical correlation analysis KCCA and of the conditional canonical correlation analysis K3CA are also elaborated. For the K2SIDLPV algorithm, the KCCA is used to extend the Akaike's stochastic time series realization theory and to obtain the LPV model identification. For the 3CKLPV algorithm the K3CA is used to identify the LPV model with exogenous inputs. A second achieved objective, based on the conformal mapping and linear fractional transformation (LFT) concepts, allows a generalized framework representation (GFR) for linear and nonlinear systems such as open loop, closed loop, time varying, nonlinear, uncertain, LPV. Exploring the GFR and the LFT representation, we present proposals for the discretization of continuous of LPV dynamic systems, specially for the discretization of uncertain or time varying sampling period, event triggered in network control. In this work the comparisons and validations of our proposals for multivariable stochastic state space LPV dynamic systems identification: ICCALPV, 3C2ILPV, K2SIDLPV and 3CKLPV with the PSBID LPV model identification method, presented good results both for elapsed time as for accuracy, as shown through examples