# Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2001)

- Volume: 21, Issue: 1, page 97-126
- ISSN: 1509-9407

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topN.U. Ahmed. "Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 21.1 (2001): 97-126. <http://eudml.org/doc/271549>.

@article{N2001,

abstract = {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.},

author = {N.U. Ahmed},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {optimal control; stochastic systems; infinite dimension; HJB equation; stationary feedback control; optimal feedback control; stochastic infinite-dimensional systems; HJB equations; distributions on Hilbert spaces},

language = {eng},

number = {1},

pages = {97-126},

title = {Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations},

url = {http://eudml.org/doc/271549},

volume = {21},

year = {2001},

}

TY - JOUR

AU - N.U. Ahmed

TI - Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2001

VL - 21

IS - 1

SP - 97

EP - 126

AB - 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.

LA - eng

KW - optimal control; stochastic systems; infinite dimension; HJB equation; stationary feedback control; optimal feedback control; stochastic infinite-dimensional systems; HJB equations; distributions on Hilbert spaces

UR - http://eudml.org/doc/271549

ER -

## References

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- [2] G. Da Prato, Perturbations of Ornstein-Uhlenbeck Transition Semigroups by a Subquadratic Potential, Communications in Applied Analysis 2 (3) (1998), 431-444. Zbl0895.93040
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- [7] S. Cerrai, A Hille-Yosida Theorem for Weakly Continuous Semigroups, Semigroup Forum 49 (1994), 349-367. Zbl0817.47048
- [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). Zbl0861.93030
- [12] N.U. Ahmed, M. Fuhrman and J. Zabczyk, On Filtering Equations in Infinite Dimensions, Journal of Functional Analysis 143 (1), 1997. Zbl0880.60043
- [13] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol 1, Theory, Kluwer Academic Publishers, Dordrecht, Boston, London 1997. Zbl0887.47001

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