Optimal control of a functional equation associated with closed range selfadjoint operators
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- by S. C. Gao and N. H. Pavel PDF
- Proc. Amer. Math. Soc. 126 (1998), 2979-2986 Request permission
Abstract:
Necessary and sufficient conditions for the optimality of a pair $(y^{*}, u^{*})$ subject to $Ay^{*} = Bu^{*} + f$ are given. Here $A$ is a selfadjoint operator with closed range on a Hilbert space $\mathcal {H}$ and $B \in L(\mathcal {H})$. The case $B$– unbounded is also discussed, which leads to some open problems. This general functional scheme includes most of the previous results on the optimal control of the $T$–periodic wave equation for all $T$ in a dense subset of $\mathbb {R}$. It also includes optimal control problems for some elliptic equations.References
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Additional Information
- S. C. Gao
- Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
- Email: shugao@bing.math.ohiou.edu
- N. H. Pavel
- Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
- Email: npavel@bing.math.ohiou.edu
- Additional Notes: The research of the first author was supported in part by the National Science Foundation of China
The research of the second author was supported in part by the National Research Fund, Korean Research Foundation Project #01-D0406 (jointly with Prof. J. K. Kim) - Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2979-2986
- MSC (1991): Primary 47N10, 47B25, 49K27
- DOI: https://doi.org/10.1090/S0002-9939-98-04633-4
- MathSciNet review: 1473668