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

L.S. Hou, J. Ming & S.D. Yang

DOI:

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 L²-norm Dirichlet control and generic, non-smooth minimum L²-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 = {}, 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 L²-norm Dirichlet control and generic, non-smooth minimum L²-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 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 KW - optimal control KW - wave equation KW - shooting method KW - 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 L²-norm Dirichlet control and generic, non-smooth minimum L²-norm Dirichlet controls.
L.S. Hou, J. Ming & S.D. Yang. (2019). 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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