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

Abstract

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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.

How to cite

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"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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