In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1019,
author = {N.U. Ahmed},
title = {Optimal control of $\infty$-dimensional stochastic systems via generalized solutions of HJB equations},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {21},
year = {2001},
pages = {97-126},
zbl = {1013.93054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1019}
}
N.U. Ahmed. Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 21 (2001) pp. 97-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1019/
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