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

Zilong Zhao (), Bogdan Robu (), Ioan Doré Landau (), Luc Dugard (), Nicolas Marchand () and Louis Job ()
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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-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
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-UGA - Institut d'études politiques de Grenoble - UGA - Université Grenoble Alpes

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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.

Keywords: MIMO models; LQR; optimal control; MIMO model; Optimal control; Macroeconomic data (search for similar items in EconPapers)
Date: 2023-06-13
Note: View the original document on HAL open archive server: https://hal.science/hal-04039452v1
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Published in ECC 2023 - 21st European Control Conference, International Federation of Automatic Control; IEEE Control Systems Society (CSS), Jun 2023, Bucarest, Romania. ⟨10.23919/ECC57647.2023.10178184⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04039452

DOI: 10.23919/ECC57647.2023.10178184

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