Nonlinear optimal control of coupled time-delayed models of economic growth

The article proposes a novel nonlinear optimal control method for the dynamics of coupled time-delayed models of economic growth. Distributed and interacting capital–labor models of economic growth are considered. Such models comprise as main variables the accumulated physical capital and labor. The interaction terms between the local models are related to the transfer of capitals between the individual economies. Each model is also characterized by time delays between its state variables and its outputs. To implement the proposed control method, the state-space description of the interconnected growth models undergoes approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. This linearization point is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the related Jacobian matrices. For the approximately linearized state-space description of the coupled time-delayed growth models, a stabilizing H-infinity (optimal) controller is designed. This controller provides the solution to the nonlinear optimal control problem for the coupled time-delayed growth models under uncertainty and perturbations. To compute the stabilizing gains of the H-infinity feedback controller, an algebraic Riccati equation is solved repetitively at each iteration of the control algorithm. The global stability properties of the proposed control scheme for the coupled time-delayed models of economic growth are proven through Lyapunov analysis.