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

In this paper, we focus on the French Macro-economic model. We use real economic data, available as time series, starting from 1980s and openly provided by the INSEE. 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 LQR to achieve that. Since we aim to maintain a constant growth rate, the control system is modified for this purpose. 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.MIMO model, LQR, Optimal control, Macroeconomic data.