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Volume 4, Issue 3-4
Shooting Methods for Numerical Solutions of Exact Controllability Problems Constrained by Linear and Semilinear 2-D Wave Equations

Sung-Dae Yang

Int. J. Numer. Anal. Mod., 4 (2007), pp. 625-647.

Published online: 2007-04

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  • 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.

  • Keywords

controllability, finite difference method, distributed control, optimal control, parallel computation, shooting method, wave equation.

  • AMS Subject Headings

93B40, 35L05, 65M06.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-625, author = {Yang , Sung-Dae}, title = {Shooting Methods for Numerical Solutions of Exact Controllability Problems Constrained by Linear and Semilinear 2-D Wave Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/881.html} }
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 -

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.

Yang , Sung-Dae. (2007). Shooting Methods for Numerical Solutions of Exact Controllability Problems Constrained by Linear and Semilinear 2-D Wave Equations. International Journal of Numerical Analysis and Modeling. 4 (3-4). 625-647. doi:
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