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Modelling and Optimal Control of MIMO System - France Macroeconomic Model Case

Author

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  • Zilong Zhao

    (GIPSA-COPERNIC - GIPSA - COntrol, PErception, Robots, navigation and Intelligent Computing - GIPSA-PSD - GIPSA Pôle Sciences des Données - GIPSA-lab - Grenoble Images Parole Signal Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

  • Bogdan Robu

    (GIPSA-MODUS - GIPSA - Modelling and Optimal Decision for Uncertain Systems - GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic - GIPSA-lab - Grenoble Images Parole Signal Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

  • Ioan Doré Landau

    (GIPSA-SAFE - GIPSA - Safe, Controlled and Monitored Systems - GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic - GIPSA-lab - Grenoble Images Parole Signal Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

  • Luc Dugard

    (GIPSA-SAFE - GIPSA - Safe, Controlled and Monitored Systems - GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic - GIPSA-lab - Grenoble Images Parole Signal Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

  • Nicolas Marchand

    (GIPSA-COPERNIC - GIPSA - COntrol, PErception, Robots, navigation and Intelligent Computing - GIPSA-PSD - GIPSA Pôle Sciences des Données - GIPSA-lab - Grenoble Images Parole Signal Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

  • Louis Job

    (PACTE - Pacte, Laboratoire de sciences sociales - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - IEPG - Sciences Po Grenoble - Institut d'études politiques de Grenoble - UGA - Université Grenoble Alpes)

Abstract

In this paper, we focus on the French Macroeconomic model. We use real economic data, available as time series,starting from 1980s and openly provided by the INSEE, the national statistics bureau of France. Variables such as Gross Domestic Production, Exportation, Importation, Household Consumption, Gross Fixed Capital Formation and Public expenditure are included in the analysis. Our objective is to maintain a constant economic growth rate according to the available resources. We implement an optimal control policy via Linear-Quadratic Regulator (LQR) to achieve that. Since we aim to maintain a constant growth rate, the control system is modified for thispurpose. We prove the efficiency with three experiments based on real data, and we test the method robustness with respect to: (1) variation of LQR parameters, (2) realistic constraints on inputs, and (3) perturbations on outputs. Results show that our designed control system can guide the output to the desired growth rate. Varying parameters of LQR can change the convergence speed of the system. Constraints on specific inputs can delay the system convergence and stimulate other inputs to compensate for the constraints. Perturbations on outputs experiment show that our control law can help the system to recover to the original statespace.

Suggested Citation

  • Zilong Zhao & Bogdan Robu & Ioan Doré Landau & Luc Dugard & Nicolas Marchand & Louis Job, 2023. "Modelling and Optimal Control of MIMO System - France Macroeconomic Model Case," Post-Print hal-04039452, HAL.
    • Handle: RePEc:hal:journl:hal-04039452
    DOI: 10.23919/ECC57647.2023.10178184
    Note: View the original document on HAL open archive server: https://hal.science/hal-04039452
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    References listed on IDEAS

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