Shooting Methods for Numerical Solutions of Exact Controllability Problems Constrained by Linear and Semilinear 2-D Wave Equations
Year: 2007
Author: Sung-Dae Yang
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 625–647
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-IJNAM-881
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 625–647
Published online: 2007-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: controllability finite difference method distributed control optimal control parallel computation shooting method wave equation.