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Optimal Control Problems with Convex Control Constraints

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Control of Coupled Partial Differential Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 155))

Abstract

We investigate optimal control problems with vector-valued controls. As model problem serve the optimal distributed control of the instationary Navier-Stokes equations. We study pointwise convex control constraints, which is a constraint of the form u(x, t) ∈ U(x, t) that has to hold on the domain Q. Here, U is an set-valued mapping that is assumed to be measurable with convex and closed images. We establish first-order necessary as well as second-order sufficient optimality conditions. And we prove regularity results for locally optimal controls.

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Author information

Authors and Affiliations

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

    Daniel Wachsmuth

Authors
  1. Daniel Wachsmuth
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Editor information

Editors and Affiliations

  1. Institute for Mathematics, University of Graz, Heinrichstraße 36, A-8010, Graz, Austria

    Karl Kunisch

  2. Institute for Mathematics, Humboldt University Berlin, Unter den Linden 6, D-10099, Berlin, Germany

    Jürgen Sprekels

  3. Institute for Applied Mathematics, University of Erlangen-Nürnberg, Martensstraße 3, D-91058, Erlangen, Germany

    Günter Leugering

  4. Institute for Mathematics, Technical University Berlin, Straße des 17 Juni 136, D-10623, Berlin, Germany

    Fredi Tröltzsch

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Wachsmuth, D. (2007). Optimal Control Problems with Convex Control Constraints. In: Kunisch, K., Sprekels, J., Leugering, G., Tröltzsch, F. (eds) Control of Coupled Partial Differential Equations. International Series of Numerical Mathematics, vol 155. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7721-2_14

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