CVA identification of nonlinear systems with LPV state-space models of affine dependence

W.E. Larimore; P.B. Cox; R. Toth

doi:10.1109/ACC.2015.7170837

CVA identification of nonlinear systems with LPV state-space models of affine dependence

W.E. Larimore
, P.B. Cox
, R. Toth

Control Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

6 Citations (Scopus)

Abstract

This paper discusses an improvement on the extension of linear subspace methods (originally developed in the Linear Time-Invariant (LTI) context) to the identification of Linear Parameter-Varying (LPV) and state-affine nonlinear system models. This includes the fitting of a special polynomial shifted form based LPV Autoregressive with eXogenous input (ARX) model to the observed input-output data. The estimated ARX model is used for filtering away the effects of future inputs on future outputs to obtain the so called "corrected future" analogous to the LTI case. The generality of the applied LPV-ARX parametrization now permits the estimation of the input-output map of a rather general class of LPV state-space models with matrices depending affinely on the scheduling. This is achieved by a canonical variate analysis (CVA) between the past and the corrected future which provides an estimate of a relevant set of state variables and their trajectories for the system, necessary for the construction of the minimal order state equations.

Original language	English
Title of host publication	Proceedings of the American Control Conference (ACC), 1-3 July 2015, Chicago, Illinois
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	831-837
Number of pages	7
ISBN (Print)	978-1-4799-8685-9
DOIs	https://doi.org/10.1109/ACC.2015.7170837
Publication status	Published - 2015
Event	2015 American Control Conference, ACC 2015 - Hilton Palmer House, Chicago, United States Duration: 1 Jul 2015 → 3 Jul 2015 http://acc2015.a2c2.org/

Conference

Conference	2015 American Control Conference, ACC 2015
Abbreviated title	ACC 2015
Country/Territory	United States
City	Chicago
Period	1/07/15 → 3/07/15
Internet address	http://acc2015.a2c2.org/

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10.1109/ACC.2015.7170837

Cite this

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title = "CVA identification of nonlinear systems with LPV state-space models of affine dependence",

abstract = "This paper discusses an improvement on the extension of linear subspace methods (originally developed in the Linear Time-Invariant (LTI) context) to the identification of Linear Parameter-Varying (LPV) and state-affine nonlinear system models. This includes the fitting of a special polynomial shifted form based LPV Autoregressive with eXogenous input (ARX) model to the observed input-output data. The estimated ARX model is used for filtering away the effects of future inputs on future outputs to obtain the so called {"}corrected future{"} analogous to the LTI case. The generality of the applied LPV-ARX parametrization now permits the estimation of the input-output map of a rather general class of LPV state-space models with matrices depending affinely on the scheduling. This is achieved by a canonical variate analysis (CVA) between the past and the corrected future which provides an estimate of a relevant set of state variables and their trajectories for the system, necessary for the construction of the minimal order state equations.",

author = "W.E. Larimore and P.B. Cox and R. Toth",

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doi = "10.1109/ACC.2015.7170837",

language = "English",

isbn = "978-1-4799-8685-9",

pages = "831--837",

booktitle = "Proceedings of the American Control Conference (ACC), 1-3 July 2015, Chicago, Illinois",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "2015 American Control Conference, ACC 2015, ACC 2015 ; Conference date: 01-07-2015 Through 03-07-2015",

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Larimore, WE, Cox, PB & Toth, R 2015, CVA identification of nonlinear systems with LPV state-space models of affine dependence. in Proceedings of the American Control Conference (ACC), 1-3 July 2015, Chicago, Illinois. Institute of Electrical and Electronics Engineers, Piscataway, pp. 831-837, 2015 American Control Conference, ACC 2015, Chicago, Illinois, United States, 1/07/15. https://doi.org/10.1109/ACC.2015.7170837

CVA identification of nonlinear systems with LPV state-space models of affine dependence. / Larimore, W.E.; Cox, P.B.; Toth, R.
Proceedings of the American Control Conference (ACC), 1-3 July 2015, Chicago, Illinois. Piscataway: Institute of Electrical and Electronics Engineers, 2015. p. 831-837.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - CVA identification of nonlinear systems with LPV state-space models of affine dependence

AU - Larimore, W.E.

AU - Cox, P.B.

AU - Toth, R.

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N2 - This paper discusses an improvement on the extension of linear subspace methods (originally developed in the Linear Time-Invariant (LTI) context) to the identification of Linear Parameter-Varying (LPV) and state-affine nonlinear system models. This includes the fitting of a special polynomial shifted form based LPV Autoregressive with eXogenous input (ARX) model to the observed input-output data. The estimated ARX model is used for filtering away the effects of future inputs on future outputs to obtain the so called "corrected future" analogous to the LTI case. The generality of the applied LPV-ARX parametrization now permits the estimation of the input-output map of a rather general class of LPV state-space models with matrices depending affinely on the scheduling. This is achieved by a canonical variate analysis (CVA) between the past and the corrected future which provides an estimate of a relevant set of state variables and their trajectories for the system, necessary for the construction of the minimal order state equations.

AB - This paper discusses an improvement on the extension of linear subspace methods (originally developed in the Linear Time-Invariant (LTI) context) to the identification of Linear Parameter-Varying (LPV) and state-affine nonlinear system models. This includes the fitting of a special polynomial shifted form based LPV Autoregressive with eXogenous input (ARX) model to the observed input-output data. The estimated ARX model is used for filtering away the effects of future inputs on future outputs to obtain the so called "corrected future" analogous to the LTI case. The generality of the applied LPV-ARX parametrization now permits the estimation of the input-output map of a rather general class of LPV state-space models with matrices depending affinely on the scheduling. This is achieved by a canonical variate analysis (CVA) between the past and the corrected future which provides an estimate of a relevant set of state variables and their trajectories for the system, necessary for the construction of the minimal order state equations.

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DO - 10.1109/ACC.2015.7170837

M3 - Conference contribution

SN - 978-1-4799-8685-9

SP - 831

EP - 837

BT - Proceedings of the American Control Conference (ACC), 1-3 July 2015, Chicago, Illinois

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - 2015 American Control Conference, ACC 2015

Y2 - 1 July 2015 through 3 July 2015

ER -

CVA identification of nonlinear systems with LPV state-space models of affine dependence

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