Approximation of Exact Boundary Controllability Problems for the 1-D Wave Equation by Optimization-Based Methods

摘要

Optimization-based numerical methods for exact boundary controllability problems for the wave equation are studied. The optimization problems are introduced in order to define unique solutions of the controllability problem. Several properties related to finite difference implementations of the methods are analyzed. Efficient implementation strategies are discussed and the convergence properties of the methods are illustrated through computational experiments. It is shown that for smooth, minimum L2-norm Dirichlet controls, the method results in convergent approximations without the need to introduce regularization. Convergent approximations are also obtained for the generic cases of non-smooth minimum L2-norm Dirichlet controls and smooth minimum fl'1-norrn Dirichlet controls. One of the strengths of the methodology is the flexibility it allows for treating other controls and other minimization criteria; such generalizations are discussed.