A COMPARISON OF REGULARIZATION METHODS FOR BOUNDARY OPTIMAL CONTROL PROBLEMS

Giorgio Bornia, Andrea Chierici, Saikanth Ratnavale

Research output: Contribution to journalArticlepeer-review

Abstract

In this work we propose and compare multiple approaches for the formulation of boundary optimal control problems constrained by PDEs. In particular, we define a property of balanced regularity that is not satisfied by traditional approaches. In order to instead guarantee this property, we consider the use of other regularization terms, one involving fractional Sobolev norms and the other one based on the introduction of lifting functions. As required by the fractional norm approach, we present a semi-analytical numerical implementation of the fractional Laplacian operator. All the proposed formulations are also considered in conjunction with con-straints of inequality type on the control variable. Numerical results are reported to compare all the presented regularization techniques.

Original languageEnglish
Pages (from-to)329-346
Number of pages18
JournalInternational Journal of Numerical Analysis and Modeling
Volume19
Issue number2-3
StatePublished - 2022

Keywords

  • Boundary optimal control
  • inequality constraints
  • regularization methods

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