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

A Kunoth, M. Schlichtenmayer & C. Schneider

DOI:

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.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-625, author = {A Kunoth, M. Schlichtenmayer and C. Schneider}, 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 - A Kunoth, M. Schlichtenmayer & C. Schneider JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 625 EP - 647 PY - 2007 DA - 2007/04 SN - 4 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/881.html KW - controllability KW - finite difference method KW - distributed control KW - optimal control KW - parallel computation KW - shooting method KW - 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.
A Kunoth, M. Schlichtenmayer & C. Schneider. (1970). 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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