Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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

Special Issues: Systemic Risk Measurement

A nonlinear optimal (H-infinity) control approach is proposed for the problem ofstabilization 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 developmentmodel is divided in two parts. The first one describes economic activities in a developed country andthe second part describes variation of economic activities in a country under development which tries tomodify its production so as to serve the needs of the developed country. The article shows that throughcontrol of the macroeconomic model of the developed country, one can finally control the dynamicsof the economy in the country under development. The control method through which this is achievedis the nonlinear H-infinity control. The macroeconomic model for the country under developmentundergoes approximate linearization round a temporary operating point. This is defined at each timeinstant by the present value of the system’s state vector and the last value of the control input vectorthat was exerted on it. The linearization is based on Taylor series expansion and the computation of theassociated 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 thecontrol 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 developmentwill finally converge to the designated reference values.
  Article Metrics

Keywords macroeconomic development models; Grossman-Helpman model; endogenous growth;nonlinear optimal control; H-infinity control; approximate linearization; Jacobian matrices; Riccatiequation; asymptotic stability

Citation: Gerasimos Rigatos, Pierluigi Siano, Taniya Ghosh, Deborah Sarno. A nonlinear optimal control approach to stabilization of a macroeconomic development model. Quantitative Finance and Economics, 2018, 2(2): 373-387. doi: 10.3934/QFE.2018.2.373


  • 1.Baldwin R, Braconier H, Forslid R (2005) Multinationals, endogenous growth, and technological spillovers: Theory and evidence. Rev Int Econ 13: 945–963.    
  • 2.Baldwin RE, Robert-Nicoud E (2008) Trade and growth with heterogeneous firms. J Int Econ 74: 21–34.    
  • 3.BarnettW, Duzhak E (2008) Non-robust dynamic inferences from macroeconomic models: Bifurcation stratification of confidence regions. Physica A 387: 3817–3825.    
  • 4.Barnett W, He Y (1998) Analysis and control of bifurcations in continuous-time macroeconomic systems, in: Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, USA.
  • 5.Barnett W, He Y (1999) Stability analysis of continuous-time macroeconometric systems. Stud nonlinear Dyn E 3: 169–188.
  • 6.Barnett W, He Y (2001a) Nonlinearity, Chaos and Bifurcations: a competition and an experiment, in: Economic Theory, Dynamics and Markets, T. NEgishi, R. Ramachandran and K. Mino Eds., Springer.
  • 7.Barnett W, He Y (2001b) Unsolved econometric problems in nonlinearity, chaos and bifurcation. Cent Eur J Oper Res 9: 147.
  • 8.Barnett W, He Y (2002) Stabilization policy as bifurcation selection: would stabilization policy work if the economy really were unstable? Macroeconomic Dynamics, Cambridge University Press 6: 713–747.
  • 9. W, He Y (2008) Bifurcations in macroeconomic models, in: Economic Growth and Macroeconomic Dynamics - Recent Developments in Economic Theory, S. Dowreck, R. Pitchford and S. Turnovsky Eds., Cambridge University Press.
  • 10.Barnetta WA, Ghosh T (2013) Bifurcation analysis of an endogenous growth model. J Econ Asymmetries 10: 53–64.    
  • 11.Barnett WA, Ghosh T (2014) Stability analysis of Uzawa-Lucas endogenous growth model. Econ Theory Bull 2: 33–44.    
  • 12.Basseville M, Nikiforov I (1993) Detection of abrupt changes: Theory and Applications. Prentice-Hall 15: 326–327.
  • 13.Blueschke D, Blueshke-Nikolaeva V, Savin I (2013) New insights into optimal control of nonlinear dynamic econometric models: application of a heuristic approach. J Econ Dyn Control 37: 821– 837.    
  • 14.Blueshke-Nikolaeva V, Blueschke D, Neck R (2012) Optimal control of nonlinear dynamic econometric models: an algorithm and an application. Comput Stat Data Analysis 56: 3230–3240.    
  • 15.Guarini G (2011) Innovation and growth in the Grossman-Helpman's model with increasing returns: a note. Econ Bull 31: 147–155.
  • 16..Harvey A, Koopman SJ (2009) Unobserved components models in economics and finance: The role of Kalman Filter in time series econometrics. IEEE Control Systems Magazine 29: 71–81.    
  • 17..Hirose K, Yamamoto K (2007) Knowledge spillovers, location of industry, and endogenous growth. Ann Regional Sci 41: 17–30.    
  • 18.Mondal D (2008) Stability analysis of the Grossman-Helpman model of endogenous product cycles. J Macroecon 30: 1302–1322.    
  • 19.Mondal D, Gupta MR (2009) Endogenous imitation and endogenous growth in a North-South model: A theoretical analysis. J Macroecon 31: 668–684.
  • 20.Platen E, Heath D (2006) A benchmark approach to quantitative finance. Springer.
  • 21.Rigatos GG (2011) Modelling and control for intelligent industrial systems: adaptive algorithms in robotcs and industrial engineering. Springer.
  • 22.Rigatos GG (2013) Advanced models of neural networks: nonlinear dynamics and stochasticity in biological neurons. Springer.
  • 23.Rigatos GG (2015) Nonlinear control and filtering using di erential flatness approaches: applications to electromechanicsl systems. Springer.
  • 24.Rigatos GG (2016) Intelligent renewable energy systems: modelling and control. Springer.
  • 25.Rigatos GG (2017) State-space approaches for modelling and control in financial engineering: systems theory and machine learning methods. Springer.
  • 26.Rigatos GG, Siano P (2015) A New Nonlinear H-infinity Feedback Control Approach to the Problem of Autonomous Robot Navigation. Intell Industrial Syst 1: 179–186.    
  • 27.Rigatos GG, Siano P, Wira P, et al. (2015) Nonlinear H-infinity Feedback Control for Asynchronous Motors of Electric Trains. Intell Industrial Syst 1: 85–98.    
  • 28.Rigatos GG, Tzafestas SG (2007) Extended Kalman Filtering for Fuzzy Modelling and Multi-Sensor Fusion, Mathematical and Computer Modelling of Dynamical Systems Taylor Francis 13: 251–266.
  • 29.Rigatos GG, Zhang Q (2009) Fuzzy model validation using the local statistical approach. Fuzzy Sets Systems 160: 882–904.    
  • 30.Sasaki H, Matsuyama J, Sako K (2013) The macroeconomic e ects of the wage gap between regular and non-regular employment and of minimum wages. Struct Change Econ Dyn 26: 61–72.    
  • 31.Shimizu T, Okawa Y, Okamoto H (2009) An analysis of income distribution between the North and the South: The Grossman-Helpman and Lai results re-examined. Rev Int Econ 16: 159–172.
  • 32.Toussaint GJ, Basar T, Bullo T (2000) H1 optimal tracking control techniques for nonlinear underactuated systems, in Proc. IEEE CDC 2000, 39th IEEE Conference on Decision and Control. Sydney Australia.
  • 33.Zhang WB (2005) Di erential Equations, Bifurcations and Chaos in Economics, Series on Advances in Mathematics for Applied Sciences. World Scientific 68.


This article has been cited by

  • 1. Dehao Ruan, Yue Liu, Generalized Halanay Inequalities with Applications to Generalized Exponential Stability and Boundedness of Time-Delay Systems, Mathematical Problems in Engineering, 2019, 2019, 1, 10.1155/2019/6072481

Reader Comments

your name: *   your email: *  

© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved