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Optimal control of systems governed by time-delayed, second-order, linear, parabolic partial differential equations with a first boundary condition

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Abstract

In this paper, we consider a class of systems governed by time-delayed, second-order, linear, parabolic partial differential equations with first boundary conditions. The existence and uniqueness of solutions of this class of systems are established in Theorem 3.2. A necessary condition for optimality for the corresponding controlled system is presented in Theorem 5.1. For the proof of this theorem, we develop several preparatory results in Sections 2, 3, and 4.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of New South Wales, Kensington, New South Wales, Australia

    K. L. Teo (Lecturer)

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  1. K. L. Teo
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Communicated by W. Fleming

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Teo, K.L. Optimal control of systems governed by time-delayed, second-order, linear, parabolic partial differential equations with a first boundary condition. J Optim Theory Appl 29, 437–481 (1979). https://doi.org/10.1007/BF00933144

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