TY - JOUR
T1 - Analysis and Approximations of a Terminal-State Optimal Control Problem Constrained by Semilinear Parabolic PDEs
AU - L. S. Hou & H.-D. Kwon
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 - <p style="text-align: justify;">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.</p>