Turnpike and Optimal Trajectories in Integral Dynamic Models with Endogenous Delay

Nonlinear optimal control of dynamic systems with endogenous time delays is analyzed. Such systems have important applications and are described by Volterra integral equations with unknowns in the integration limits. The paper focuses on the structure and asymptotic behavior of solutions to several optimization problems with endogenous delay. It is shown that, in certain cases, a special delay trajectory exists and attracts the optimal solution. In economics, such behavior corresponds to the turnpike properties of the optimal lifetime of capital in vintage capital models.

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