VECTOR-VALUED MULTIBANG CONTROL OF DIFFERENTIAL EQUATIONS

摘要

We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to take values pointwise in a finite set M subset of R-m. After convex relaxation, one obtains a well-posed optimization problem, which still promotes control values in M. We state the corresponding well-posedness and stability analysis and exemplify the results for two specific cases of quite general interest, optimal control of the Bloch equation and optimal control of an elastic deformation. We finally formulate a semismooth Newton method to numerically solve a regularized version of the optimal control problem and illustrate the behavior of the approach for our example cases.