In optimal control problems frequently pointwise control constraints appear. We consider a finite string that is fixed at one end and controlled via Dirichlet conditions at the other end with a given upper bound M for the L∞-norm of the control. The problem is to control the string to the zero state in a given finite time. If M is too small, no feasible control exists. If M is large enough, the optimal control problem to find an admissible control with minimal L2-norm has a solution that we present in this paper.
A finite difference discretization of the optimal control problem is considered and we prove that for Lipschitz continuous data the discretization error is of the order of the stepsize.
Optimal control Boundary control Dirichlet control Wave equation Control constraints Discretization Finite differences Discretization error
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