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Pré-Publication, Document De Travail Année : 2022

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

Résumé

Applying control theory to economic problems has been studied since 1970s. Early stage studies focus on policy analysis and optimizations. With the development of theory, recent researches touch on more applications such as (1) monetary policy, (2) fiscal policy, and (3) resource allocation problems using PID control and optimal control. Even the problems change, the studies that applied optimal control follow the same idea: finding a control law to optimize an objective function for a dynamic system under certain constraints. In this paper, we focus on french macroeconomic model. 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 a one-of-a-kind optimal control via Linear-Quadratic regulator (LQR) to achieve that. Since we aim to maintain a constant growth rate instead of a constant value, a specific control system is designed for this purpose. We implement three experiments: (1) variation on parameter of LQR, (2) 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 state-space.
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Dates et versions

hal-03632679 , version 1 (06-04-2022)

Identifiants

  • HAL Id : hal-03632679 , version 1

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Zilong Zhao, Bogdan Robu, Ioan Doré Landau, Luc Dugard, Nicolas Marchand, et al.. Modelling and Optimal Control of MIMO System -France Macroeconomic Model Case. 2022. ⟨hal-03632679⟩
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