JournalszaaVol. 20, No. 2pp. 395–429

On SS-Homogenization of an Optimal Control Problem with Control and State Constraints

  • Peter I. Kogut

    Dnipropetrovsk National University, Ukraine
  • Günter Leugering

    Universität Erlangen-Nürnberg, Germany
On $S$-Homogenization of an Optimal Control Problem with Control and State Constraints cover
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Abstract

We study the limiting behavior of an optimal control problem for a linear elliptic equation subject to control and state constraints. Each constituent of the mathematical description of such an optimal control problem may depend on a small parameter ϵ\epsilon. We study the limit of this problem when ϵ0\epsilon \rightarrow 0 in the framework of variational SS-convergence which generalizes the concept of Γ\Gamma-convergence. We also introduce the notion of GG*-convergence generalizing the concept of GG-convergence to operators with constraints. We show convergence of the sequence of optimal control problems and identify its limit. We then apply the theory to an elliptic problem on a perforated domain.

Cite this article

Peter I. Kogut, Günter Leugering, On SS-Homogenization of an Optimal Control Problem with Control and State Constraints. Z. Anal. Anwend. 20 (2001), no. 2, pp. 395–429

DOI 10.4171/ZAA/1023