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Maximum principle of optimal periodic control for functional differential systems

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Abstract

This paper discusses the optimal periodic control problem to minimize the cost function

$$J(u) = \int_0^1 {g(t,x(t),u(t))dt} $$

subject to the functional differential system

$$dx(t)/dt = f(t,x_t ,u(t)),x_1 = x_0 $$

andu(·) εU ad. The maximum principle as a necessary condition of optimal control is proved under the assumption that Eq. (4) and its adjoint equation (5) both have no nontrivial periodic solution with period of 1. In this paper, the control domainU is an arbitrary set inR m.

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Authors and Affiliations

  1. Department of Mathematics, Fudan University, Shanghai, China

    X. J. Li (Professor)

  2. Division of Applied Mathematics, Brown University, Providence, Rhode Island

    X. J. Li (Professor)

Authors
  1. X. J. Li
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Communicated by L. D. Berkovitz

This work was supported by the Science Fund of the Chinese Academy of Sciences and the Research Fund of Brown University.

The author would like to thank Professors H. T. Banks, L. D. Berkovitz, W. H. Fleming, and J. K. Hale for their hospitality and helpful discussions.

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Li, X.J. Maximum principle of optimal periodic control for functional differential systems. J Optim Theory Appl 50, 421–429 (1986). https://doi.org/10.1007/BF00938629

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