Geodesic
Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 21 (2001) no. 1, pp. 97-126.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: optimal control, stochastic systems, infinite dimension, HJB equation, stationary feedback control 
@article{DMDICO_2001_21_1_a3,
     author = {Ahmed, N.},
     title = {Optimal control of \ensuremath{\infty}-dimensional stochastic systems via generalized solutions of {HJB} equations},
     journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization},
     pages = {97--126},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2001},
     zbl = {1013.93054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMDICO_2001_21_1_a3/}
}
TY  - JOUR
AU  - Ahmed, N.
TI  - Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations
JO  - Discussiones Mathematicae. Differential Inclusions, Control and Optimization
PY  - 2001
SP  - 97
EP  - 126
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMDICO_2001_21_1_a3/
LA  - en
ID  - DMDICO_2001_21_1_a3
ER  - 
%0 Journal Article
%A Ahmed, N.
%T Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations
%J Discussiones Mathematicae. Differential Inclusions, Control and Optimization
%D 2001
%P 97-126
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMDICO_2001_21_1_a3/
%G en
%F DMDICO_2001_21_1_a3
Ahmed, N. Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 21 (2001) no. 1, pp. 97-126. http://geodesic.mathdoc.fr/item/DMDICO_2001_21_1_a3/

[1] F. Gozzi and E. Rouy, Regular Solutions of Second-Order Stationary Hamilton-Jacobi Equations, Journal of Differential Equations 130 (1996), 210-234.

[2] G. Da Prato, Perturbations of Ornstein-Uhlenbeck Transition Semigroups by a Subquadratic Potential, Communications in Applied Analysis 2 (3) (1998), 431-444.

[3] B. Goldys and B. Maslowski, Ergodic Control of Semilinear Stochastic Equations and Hamilton-Jacobi Equations, preprint, (1998).

[4] G. Da Prato and J. Zabczyk, Regular Densities of Invariant Measures in Hilbert Spaces, Journal of Functional Analysis 130 (1995), 427-449.

[5] G. Da Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems, London Mathematical Society Lecture Note, 229, Cambridge University Press 1996.

[6] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimension, Encyclopedia of Mathematics and its Applications series, 44, Cambridge University Press 1992.

[7] S. Cerrai, A Hille-Yosida Theorem for Weakly Continuous Semigroups, Semigroup Forum 49 (1994), 349-367.

[8] N.U. Ahmed and J. Zabczyk, Nonlinear Filtering for Semilinear Stochastic Differential Equations on Hilbert Spaces, Preprint 522, Inst. Math. Polish Academy of Sciences, Warsaw, Poland.

[9] N.U. Ahmed, Relaxed Controls for Stochastic Boundary Value Problems in Infinite Dimension, Lect. Notes in Contr. and Inf. Sciences 149 (1990), 1-10.

[10] N.U. Ahmed, Optimal Relaxed Controls for Nonlinear Infinite Dimensional Stochastic Differential Inclusions, International Symposium on Optimal Control of infinite Dimensional Systems, (ed. N.H. Pavel), Lect. Notes in Pure and Applied Math, Marcel Dekker, New York and Basel 160 (1994), 1-19.

[11] N.U. Ahmed, Optimal Relaxed Controls for Infinite Dimensional Stochastic Systems of Zakai Type, SIAM J. Control and Optimization 34 (5) (1996).

[12] N.U. Ahmed, M. Fuhrman and J. Zabczyk, On Filtering Equations in Infinite Dimensions, Journal of Functional Analysis 143 (1), 1997.

[13] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol 1, Theory, Kluwer Academic Publishers, Dordrecht, Boston, London 1997.