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Volume 13, Issue 1
Numerical Shooting Methods for Optimal Boundary Control and Exact Boundary Control of 1-D Wave Equations

L. S. Hou & S.-D. Yang

Int. J. Numer. Anal. Mod., 13 (2016), pp. 122-144.

Published online: 2016-01

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  • Abstract

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.

  • Keywords

Controllability, optimal control, wave equation, shooting method, finite difference method.

  • AMS Subject Headings

93B40, 35L05, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-122, author = {Hou , L. S. and Yang , S.-D.}, title = {Numerical Shooting Methods for Optimal Boundary Control and Exact Boundary Control of 1-D Wave Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {1}, pages = {122--144}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/430.html} }
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 -

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.

Hou , L. S. and Yang , S.-D.. (2016). Numerical Shooting Methods for Optimal Boundary Control and Exact Boundary Control of 1-D Wave Equations. International Journal of Numerical Analysis and Modeling. 13 (1). 122-144. doi:
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