Abstract
This paper is concerned with optimal control of semilinear stochastic evolution equations on Hilbert space driven by stochastic vector measure. Both continuous and discontinuous (measurable) vector fields are admitted. Due to nonexistence of regular solutions, existence and uniqueness of generalized (or measure valued) solutions are proved. Using these results, existence of optimal feedback controls from the class of bounded Borel measurable maps are proved for several interesting optimization problems.
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N.U. Ahmed. Measure Solutions for Semi-linear Evolution Equations with Polynomial Growth and Their Optimal Controls. Discussiones Mathematicae, Differential Inclusions., 17, 5–27, 1997.
N.U. Ahmed. Measure Solutions for Semilinear Systems with Unbounded Nonlinearities. Nonlinear Analysis: Theory, Methods and Applications, 35, 487–503, 1999.
N.U. Ahmed. Relaxed Solutions for Stochastic Evolution Equations on Hilbert Space with Polynomial Nonlinearities. Publicationes Mathematicae, Debrecen, 54(1–2), 75–101, 1999.
N.U. Ahmed. Measure Solutions for Evolution Equations with Discontinuous Vector Fields. Nonlinear Functional analysis and Applications. 9(3), 467–484, 2004.
N.U. Ahmed. Measure Solutions for Impulsive Evolution Equations with Measurable Vector Fields. Journal of Math. Annal. and Appl, 2004 (submitted).
N.U. Ahmed. Measure Valued Solutions for Stochastic Evolution Equations on Hilbert Space and Their Feedback Control. Discussiones Mathematicae, D1CO, 2005, 25 (to appear).
S. Cerrai. Elliptic and parabolic equations in R n with coefficients having polynomial growth. Preprints di Matematica, n.9, Scuola Normale Superiore, Pisa, 1995.
G. Da Prato and J. Zabczyk. Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and its Applications, 44, Cambridge University Press, 1992.
J. Diestel and J.J. Uhl, Jr. Vector Measures. Math. Surveys Monogr. 15, AMS, Providence, RI, 1977.
N. Dunford and J.T. Schwartz. Linear Operators, Part 1. Interscience Publishers, Inc., New York, 1958.
H. Fattorini. A Remark on Existence of solutions of Infinite Dimensional Non-compact Optimal Control Problems, SIAM J. Control and Optim. 35(4), 1422–1433, 1997.
I. Gyongy and N.V. Krylov. On Stochastic Equations with Respect to Semimartingales, Stochastics no. 1, 1–21, 1980/81.
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Ahmed, N.U. (2006). Optimal Stochastic Control of Measure Solutions on Hilbert Space. In: Ceragioli, F., Dontchev, A., Furuta, H., Marti, K., Pandolfi, L. (eds) Systems, Control, Modeling and Optimization. CSMO 2005. IFIP International Federation for Information Processing, vol 202. Springer, Boston, MA . https://doi.org/10.1007/0-387-33882-9_1
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DOI: https://doi.org/10.1007/0-387-33882-9_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-33881-1
Online ISBN: 978-0-387-33882-8
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