# Stochastic diffrential equations on Banach spaces and their optimal feedback control

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2012)

- Volume: 32, Issue: 1, page 87-109
- ISSN: 1509-9407

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top"Stochastic diffrential equations on Banach spaces and their optimal feedback control." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 32.1 (2012): 87-109. <http://eudml.org/doc/270218>.

@article{Unknown2012,

abstract = {In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems. We present results on existence of optimal feedback operators.},

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

keywords = {stochastic differential equations; Banach spaces; optimal feedback control; objective functionals; Lévy-Prohorov metric; Hausdorff dimension; time-optimal problems},

language = {eng},

number = {1},

pages = {87-109},

title = {Stochastic diffrential equations on Banach spaces and their optimal feedback control},

url = {http://eudml.org/doc/270218},

volume = {32},

year = {2012},

}

TY - JOUR

TI - Stochastic diffrential equations on Banach spaces and their optimal feedback control

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2012

VL - 32

IS - 1

SP - 87

EP - 109

AB - In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems. We present results on existence of optimal feedback operators.

LA - eng

KW - stochastic differential equations; Banach spaces; optimal feedback control; objective functionals; Lévy-Prohorov metric; Hausdorff dimension; time-optimal problems

UR - http://eudml.org/doc/270218

ER -

## References

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