Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Optimal control of a functional equation
associated with closed range
selfadjoint operators


Authors: S. C. Gao and N. H. Pavel
Journal: Proc. Amer. Math. Soc. 126 (1998), 2979-2986
MSC (1991): Primary 47N10, 47B25, 49K27.
MathSciNet review: 1473668
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Abstract | References | Similar Articles | Additional Information

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 $B \in L(\cal{H})$. 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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04633-4
Keywords: Self-adjoint operators with closed range, optimal pairs, maximum principles, periodic waves
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
Article copyright: © Copyright 1998 American Mathematical Society