"Fixing a Regularity Mismatch in PDE-constrained Boundary Control Problems"
Department of Mathematics and Statistics
Texas Tech University
A mismatch between the regularity of solutions of partial differential equations and their boundary data is commonly encountered once these PDE systems act as constraints within a boundary optimal control framework. This mismatch is essentially the result of a lack of computability of norms in fractional Sobolev spaces. In this talk we discuss a reformulation of boundary control problems with an extension approach whose first goal is to fix this regularity mismatch.Moreover, this approach provides additional benefits when applied to constraints characterized by compatibility conditions on the boundary data, such as those arising for the incompressible Navier-Stokes equations. The fulfillment of compatibility conditions can be achieved with a control constraint that turns dense enforcements into sparse ones, thus obtaining a more favorable numerical implementation. We discuss the use of the extension approach for some classes of boundary control problems constrained by multiphysics systems in fluid dynamics. Numerical strategies are discussed and computational results are presented. We also provide a perspective on other approaches that may be considered for tackling similar goals.