TY - JOUR
T1 - Numerical Shooting Methods for Optimal Boundary Control and Exact Boundary Control of 1-D Wave Equations
AU - Hou , L. S.
AU - Yang , S.-D.
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 122
EP - 144
PY - 2016
DA - 2016/01
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/430.html
KW - Controllability, optimal control, wave equation, shooting method, finite difference method.
AB - <p style="text-align: justify;">Numerical solutions of optimal Dirichlet boundary control problems for linear and
semilinear wave equations are studied. The optimal control problem is reformulated as a system
of equations (an optimality system) that consists of an initial value problem for the underlying
(linear or semilinear) wave equation and a terminal value problem for the adjoint wave equation.
The discretized optimality system is solved by a shooting method. The convergence properties
of the numerical shooting method in the context of exact controllability are illustrated through
computational experiments. In particular, in the case of the linear wave equation, convergent
approximations are obtained for both smooth minimum $L^2$-norm Dirichlet control and generic,
non-smooth minimum $L^2$-norm Dirichlet controls.</p>