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Volume 4, Issue 3-4
Analysis and Approximations of a Terminal-State Optimal Control Problem Constrained by Semilinear Parabolic PDEs

L. S. Hou & H.-D. Kwon

Int. J. Numer. Anal. Mod., 4 (2007), pp. 713-728.

Published online: 2007-04

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  • Abstract

A terminal-state optimal control problem for semilinear parabolic equations is studied in this paper. The control objective is to track a desired terminal state and the control is of the distributed type. A distinctive feature of this work is that the controlled state and the target state are allowed to have nonmatching boundary conditions. The existence of an optimal control solution is proved. We also show that the optimal solution depending on a parameter $\gamma$ gives solutions to the approximate controllability problem as $\gamma \rightarrow 0$. Error estimates are obtained for semidiscrete (spatially discrete) approximations of the optimal control problem. A gradient algorithm is discussed and numerical results are presented.

  • Keywords

terminal-state tracking, optimal control, semilinear parabolic equations, approximate controllability.

  • AMS Subject Headings

93B05, 93B06, 93B40, 93C20, 93C50, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-713, author = {}, title = {Analysis and Approximations of a Terminal-State Optimal Control Problem Constrained by Semilinear Parabolic PDEs}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {713--728}, abstract = {

A terminal-state optimal control problem for semilinear parabolic equations is studied in this paper. The control objective is to track a desired terminal state and the control is of the distributed type. A distinctive feature of this work is that the controlled state and the target state are allowed to have nonmatching boundary conditions. The existence of an optimal control solution is proved. We also show that the optimal solution depending on a parameter $\gamma$ gives solutions to the approximate controllability problem as $\gamma \rightarrow 0$. Error estimates are obtained for semidiscrete (spatially discrete) approximations of the optimal control problem. A gradient algorithm is discussed and numerical results are presented.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/885.html} }
TY - JOUR T1 - Analysis and Approximations of a Terminal-State Optimal Control Problem Constrained by Semilinear Parabolic PDEs JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 713 EP - 728 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/885.html KW - terminal-state tracking, optimal control, semilinear parabolic equations, approximate controllability. AB -

A terminal-state optimal control problem for semilinear parabolic equations is studied in this paper. The control objective is to track a desired terminal state and the control is of the distributed type. A distinctive feature of this work is that the controlled state and the target state are allowed to have nonmatching boundary conditions. The existence of an optimal control solution is proved. We also show that the optimal solution depending on a parameter $\gamma$ gives solutions to the approximate controllability problem as $\gamma \rightarrow 0$. Error estimates are obtained for semidiscrete (spatially discrete) approximations of the optimal control problem. A gradient algorithm is discussed and numerical results are presented.

L. S. Hou & H.-D. Kwon. (1970). Analysis and Approximations of a Terminal-State Optimal Control Problem Constrained by Semilinear Parabolic PDEs. International Journal of Numerical Analysis and Modeling. 4 (3-4). 713-728. doi:
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