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Turnpike and Optimal Trajectories in Integral Dynamic Models with Endogenous Delay

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Abstract

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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Authors and Affiliations

  1. Associate Professor, Department of Mathematics, Prairie View A&M University, Prairie View, Texas, USA

    N. Hritonenko

  2. Associate Professor, College of Business and Economics, Houston Baptist University, Houston, Texas, USA

    Yu. Yatsenko

Authors
  1. N. Hritonenko
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  2. Yu. Yatsenko
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Additional information

The authors thank Professor F. Chernousko for his kind assistance and Professor W. Trotti for a supporting grant from Prairie View A&M University.

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Hritonenko, N., Yatsenko, Y. Turnpike and Optimal Trajectories in Integral Dynamic Models with Endogenous Delay. J Optim Theory Appl 127, 109–127 (2005). https://doi.org/10.1007/s10957-005-6395-2

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