Abstract

A level-set shape optimization approach to the solution of a state-constrained optimal control problem.

Wolfgang Ring
University of Graz
Special Research Center on Optimzation and Control, Institute of

For a state constrained optimal control problem
the active set with respect to the constraint
can be considered as the primary unknown variable.
In fact, the first order optimality conditions in primal-dual form lead to a free boundary problem with the active set acting as the unknown domain on which an overdetermined boundary value problem must be satisfied. We relax the surplus boundary condition and determine the active set by solving a shape optimization problem. The algorithm which is used to find the optimal shape is based on the
level set methodology. The speed function involved in the level set equation for propagating the interface is computed by utilizing techniques from classical shape
optimization.