Realization and identification algorithm for stochastic LPV state-space models with exogenous inputs

In this paper, we present a realization and an identification algorithm for stochastic Linear Parameter-Varying State-Space Affine (LPV-SSA) representations. The proposed realization algorithm combines the deterministic LPV input output to LPV state-space realization scheme based on correlation analysis with a stochastic covariance realization algorithm. Based on this realization algorithm, a computationally efficient and statistically consistent identification algorithm is proposed to estimate the LPV model matrices, which are computed from the empirical covariance matrices of outputs, inputs and scheduling signal observations. The effectiveness of the proposed algorithm is shown via a numerical case study.

[1]  Hossam Seddik Abbas,et al.  On the State-Space Realization of LPV Input-Output Models: Practical Approaches , 2012, IEEE Transactions on Control Systems Technology.

[2]  Paulo J. Lopes dos Santos,et al.  Identification of Bilinear Systems With White Noise Inputs: An Iterative Deterministic-Stochastic Subspace Approach , 2009, IEEE Transactions on Control Systems Technology.

[3]  Roland Tóth,et al.  Realization Theory for LPV State-Space Representations With Affine Dependence , 2016, IEEE Transactions on Automatic Control.

[4]  Roland Toth,et al.  Modeling and Identification of Linear Parameter-Varying Systems , 2010 .

[5]  Michel Verhaegen,et al.  Subspace identification of Bilinear and LPV systems for open- and closed-loop data , 2009, Autom..

[6]  Alberto Bemporad,et al.  A bias-correction method for closed-loop identification of Linear Parameter-Varying systems , 2018, Autom..

[7]  Marco Lovera,et al.  Identification of LPV State Space Models for Autonomic Web Service Systems , 2011, IEEE Transactions on Control Systems Technology.

[8]  Hugues Garnier,et al.  Refined instrumental variable methods for identification of LPV Box-Jenkins models , 2010, Autom..

[9]  Bassam Bamieh,et al.  Identification of linear parameter varying models , 2002 .

[10]  Bart De Moor,et al.  Subspace identification of bilinear systems subject to white inputs , 1999, IEEE Trans. Autom. Control..

[11]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.

[12]  Michel Verhaegen,et al.  Subspace identification of MIMO LPV systems using a periodic scheduling sequence , 2007, Autom..

[13]  M. B. Reed,et al.  Realization Theory of Discrete-Time Nonlinear Systems: Part I - The Bounded Case , 1979 .

[14]  René Vidal,et al.  Realization Theory for a Class of Stochastic Bilinear Systems , 2018, IEEE Transactions on Automatic Control.

[15]  P. Spreij.  Probability and Measure , 1996 .

[16]  P. Billingsley,et al.  Probability and Measure , 1980 .

[17]  Roland Tóth,et al.  Towards Efficient Maximum Likelihood Estimation of LPV-SS Models , 2018, Autom..

[18]  Pb Pepijn Cox,et al.  Estimation of LPV-SS models with static dependency , 2015 .

[19]  Roland Tóth,et al.  LPV system identification under noise corrupted scheduling and output signal observations , 2015, Autom..

[20]  J. H. vanSchuppen,et al.  Invariance properties of the conditional independence relation , 1983 .

[21]  Jean Berstel,et al.  Rational series and their languages , 1988, EATCS monographs on theoretical computer science.

[22]  Vincent Verdult,et al.  Kernel methods for subspace identification of multivariable LPV and bilinear systems , 2005, Autom..

[23]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .

[24]  Manas Mejari,et al.  Consistent and computationally efficient estimation for stochastic LPV state-space models: realization based approach , 2019, 2019 IEEE 58th Conference on Decision and Control (CDC).