Flatness-based control and Kalman filtering for a continuous-time macroeconomic model

G. Rigatos; P. Siano; T. Ghosh; K. Busawon; R. Binns

doi:10.1063/1.5012323

Flatness-based control and Kalman filtering for a continuous-time macroeconomic model

G. Rigatos, P. Siano, T. Ghosh, K. Busawon, R. Binns

Mathematics, Physics and Electrical Engineering

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

1 Citation (Scopus)

Abstract

The article proposes flatness-based control for a nonlinear macro-economic model of the UK economy. The differential flatness properties of the model are proven. This enables to introduce a transformation (diffeomorphism) of the system's state variables and to express the state-space description of the model in the linear canonical (Brunowsky) form in which both the feedback control and the state estimation problem can be solved. For the linearized equivalent model of the macroeconomic system, stabilizing feedback control can be achieved using pole placement methods. Moreover, to implement stabilizing feedback control of the system by measuring only a subset of its state vector elements the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized equivalent model of the financial system and of an inverse transformation that is based again on differential flatness theory. The asymptotic stability properties of the control scheme are confirmed.

Original language	English
Title of host publication	Proceedings of the International Conference of Computational Methods in Sciences and Engineering 2017, ICCMSE 2017
Publisher	American Institute of Physics
Volume	1906
ISBN (Electronic)	9780735415966
DOIs	https://doi.org/10.1063/1.5012323
Publication status	Published - 28 Nov 2017
Event	International Conference of Computational Methods in Sciences and Engineering 2017, ICCMSE 2017 - Thessaloniki, Greece Duration: 21 Apr 2017 → 25 Apr 2017

Conference

Conference	International Conference of Computational Methods in Sciences and Engineering 2017, ICCMSE 2017
Country/Territory	Greece
City	Thessaloniki
Period	21/04/17 → 25/04/17

Keywords

approximate linearization
asymptotic stability
chaotic finance dynamics
H-infinity control
nonlinear optimal control
Riccati equation
Taylor series expansion

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10.1063/1.5012323

Cite this

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title = "Flatness-based control and Kalman filtering for a continuous-time macroeconomic model",

abstract = "The article proposes flatness-based control for a nonlinear macro-economic model of the UK economy. The differential flatness properties of the model are proven. This enables to introduce a transformation (diffeomorphism) of the system's state variables and to express the state-space description of the model in the linear canonical (Brunowsky) form in which both the feedback control and the state estimation problem can be solved. For the linearized equivalent model of the macroeconomic system, stabilizing feedback control can be achieved using pole placement methods. Moreover, to implement stabilizing feedback control of the system by measuring only a subset of its state vector elements the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized equivalent model of the financial system and of an inverse transformation that is based again on differential flatness theory. The asymptotic stability properties of the control scheme are confirmed.",

keywords = "approximate linearization, asymptotic stability, chaotic finance dynamics, H-infinity control, nonlinear optimal control, Riccati equation, Taylor series expansion",

author = "G. Rigatos and P. Siano and T. Ghosh and K. Busawon and R. Binns",

year = "2017",

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booktitle = "Proceedings of the International Conference of Computational Methods in Sciences and Engineering 2017, ICCMSE 2017",

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Rigatos, G, Siano, P, Ghosh, T, Busawon, K & Binns, R 2017, Flatness-based control and Kalman filtering for a continuous-time macroeconomic model. in Proceedings of the International Conference of Computational Methods in Sciences and Engineering 2017, ICCMSE 2017. vol. 1906, 060005, American Institute of Physics, International Conference of Computational Methods in Sciences and Engineering 2017, ICCMSE 2017, Thessaloniki, Greece, 21/04/17. https://doi.org/10.1063/1.5012323

Flatness-based control and Kalman filtering for a continuous-time macroeconomic model. / Rigatos, G.; Siano, P.; Ghosh, T. et al.
Proceedings of the International Conference of Computational Methods in Sciences and Engineering 2017, ICCMSE 2017. Vol. 1906 American Institute of Physics, 2017. 060005.

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

TY - GEN

T1 - Flatness-based control and Kalman filtering for a continuous-time macroeconomic model

AU - Rigatos, G.

AU - Siano, P.

AU - Ghosh, T.

AU - Busawon, K.

AU - Binns, R.

PY - 2017/11/28

Y1 - 2017/11/28

N2 - The article proposes flatness-based control for a nonlinear macro-economic model of the UK economy. The differential flatness properties of the model are proven. This enables to introduce a transformation (diffeomorphism) of the system's state variables and to express the state-space description of the model in the linear canonical (Brunowsky) form in which both the feedback control and the state estimation problem can be solved. For the linearized equivalent model of the macroeconomic system, stabilizing feedback control can be achieved using pole placement methods. Moreover, to implement stabilizing feedback control of the system by measuring only a subset of its state vector elements the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized equivalent model of the financial system and of an inverse transformation that is based again on differential flatness theory. The asymptotic stability properties of the control scheme are confirmed.

AB - The article proposes flatness-based control for a nonlinear macro-economic model of the UK economy. The differential flatness properties of the model are proven. This enables to introduce a transformation (diffeomorphism) of the system's state variables and to express the state-space description of the model in the linear canonical (Brunowsky) form in which both the feedback control and the state estimation problem can be solved. For the linearized equivalent model of the macroeconomic system, stabilizing feedback control can be achieved using pole placement methods. Moreover, to implement stabilizing feedback control of the system by measuring only a subset of its state vector elements the Derivative-free nonlinear Kalman Filter is used. This consists of the Kalman Filter recursion applied on the linearized equivalent model of the financial system and of an inverse transformation that is based again on differential flatness theory. The asymptotic stability properties of the control scheme are confirmed.

KW - approximate linearization

KW - asymptotic stability

KW - chaotic finance dynamics

KW - H-infinity control

KW - nonlinear optimal control

KW - Riccati equation

KW - Taylor series expansion

U2 - 10.1063/1.5012323

DO - 10.1063/1.5012323

M3 - Conference contribution

AN - SCOPUS:85038814059

VL - 1906

BT - Proceedings of the International Conference of Computational Methods in Sciences and Engineering 2017, ICCMSE 2017

PB - American Institute of Physics

T2 - International Conference of Computational Methods in Sciences and Engineering 2017, ICCMSE 2017

Y2 - 21 April 2017 through 25 April 2017

ER -

Flatness-based control and Kalman filtering for a continuous-time macroeconomic model

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Conference

Keywords

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