Abstract
We consider the approximate optimal control based on the principle of feedback relation (synthesis) for a parabolic boundary-value problem. We represent the feedback operator as Fourier series in the eigenfunctions of the Laplace operator, which does not enable us to use these results in practice. In view of this fact, we justify the convergence of approximate controls, switching points, and values of the quality criterion to the exact values of the corresponding variables.
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Kapustyan, O.A. Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem. Ukrainian Mathematical Journal 54, 2067–2074 (2002). https://doi.org/10.1023/A:1024089702245
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DOI: https://doi.org/10.1023/A:1024089702245