A flatness-based adaptive fuzzy control method for an endogenous economic growth model

Abstract

The article proposes a flatness-based adaptive control approach for the Uzawa-Lucas financial growth model. This model describes interaction between physical and human capital within an economy and so far equilibria and bifurcations have been computed about it. With the article’s developments the problem of control and stabilization of the Uzawa-Lucas growth dynamics is solved through the application of exogenous control inputs and after considering uncertainty and unknown parameters for the related state-space model. It is proven that the Uzawa-Lucas state-space model is differentially flat and its transformation into an equivalent input-output linearized form is achieved. For the latter description of this financial system an indirect adaptive fuzzy control method is developed. The method relies on feedback of only the system’s output and accomplishes simultaneously the estimation of unknown dynamics of the growth model as well as the convergence of the state variables to the defined setpoints. Learning of the unknown dynamics is performed through neurofuzzy approximators which are iteratively updated with the use of gradient algorithms. Since only feedback of the system’s output is used, state vector estimation was performed with the use of a convergent state observer. The computation of the gains of the adaptive fuzzy controller required the solution of two algebraic Riccati equations. The global asymptotic stability properties of the control method are proven through Lyapunov analysis.