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Some aspects of reachability for parabolic boundary control problems with control constraints

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Abstract

A class of one-dimensional parabolic optimal boundary control problems is considered. The discussion includes Neumann, Robin, and Dirichlet boundary conditions. The reachability of a given target state in final time is discussed under box constraints on the control. As a mathematical tool, related exponential moment problems are investigated. Moreover, based on a detailed study of the adjoint state, a technique is presented to find the location and the number of the switching points of optimal bang-bang controls. Numerical examples illustrate this procedure.

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  1. Institut für Mathematik, Technische Universität Berlin, Str. des 17. Juni 136, 10623, Berlin, Germany

    Vili Dhamo & Fredi Tröltzsch

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  1. Vili Dhamo
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  2. Fredi Tröltzsch
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Correspondence to Vili Dhamo.

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Dhamo, V., Tröltzsch, F. Some aspects of reachability for parabolic boundary control problems with control constraints. Comput Optim Appl 50, 75–110 (2011). https://doi.org/10.1007/s10589-009-9310-1

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