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Solutions for a class of optimal control problems with time delay, part 2

Abstract

In this work, we analyze the structure of optimal solutions for a class of optimal control problems with time delay whose state is governed by a nonlinear autonomous Volterra integrodifferential equation. We establish that an almost optimal finite trajectory defined on an interval [0, τ] is contained in a small neighborhood of the optimal steady state for all\(t \in \left[ {\bar T,\tau - \bar T} \right]\), where\(\bar T\) is a constant which depends on the neighborhood and does not depend on τ.

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Additional information

The author thanks A. Leizarowitz for fruitful discussions.

Communicated by L. D. Berkovitz

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Zaslavski, A.J. Solutions for a class of optimal control problems with time delay, part 2. J Optim Theory Appl 91, 455–490 (1996). https://doi.org/10.1007/BF02190105

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Key Words

  • Integrodifferential equations
  • optimal steady state
  • turnpike property