A nonlinear optimal control approach to stabilization of a macroeconomic development model

Gerasimos Rigatos; Pierluigi Siano; Taniya Ghosh; Deborah Sarno; Gerasimos Rigatos; Pierluigi Siano; Taniya Ghosh; Deborah Sarno

doi:10.3934/QFE.2018.2.373

Quantitative Finance and Economics

2018, Volume 2, Issue 2: 373-387. doi: 10.3934/QFE.2018.2.373

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A nonlinear optimal control approach to stabilization of a macroeconomic development model

1.
Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion Patras, Greece
2.
Department of Industrial Engineering, University of Salerno, 54094, Fisciano, Italy
3.
IGIDR, Institute of Development Research, 400065, Mumbai, India

Received: 12 November 2017 Accepted: 06 March 2018 Published: 31 May 2018
JEL Codes: C61, E00

A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.
Citation: Gerasimos Rigatos, Pierluigi Siano, Taniya Ghosh, Deborah Sarno. A nonlinear optimal control approach to stabilization of a macroeconomic development model[J]. Quantitative Finance and Economics, 2018, 2(2): 373-387. doi: 10.3934/QFE.2018.2.373

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Abstract

A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.

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