TY - JOUR
T1 - Shooting Methods for Numerical Solutions of Exact Controllability Problems Constrained by Linear and Semilinear 2-D Wave Equations
AU - Yang , Sung-Dae
JO - International Journal of Numerical Analysis and Modeling
VL - 3-4
SP - 625
EP - 647
PY - 2007
DA - 2007/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/881.html
KW - controllability, finite difference method, distributed control, optimal control, parallel computation, shooting method, wave equation.
AB - <p style="text-align: justify;">Numerical solutions of exact controllability problems for
linear and semilinear 2-d wave equations with distributed controls are
studied. Exact controllability problems can be solved by the
corresponding optimal control problems. 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.</p>